propiedades de particula · •1879: ley de stefan-boltzmann, •1893: ley de desplazamiento de...

Propiedades Corpusculares de la Radiación

Electromagnética

Introducción a la Física Cuántica, 2019-2

Marzo de 2019

¿Cuál fue la primera cantidad física en ser cuantizada?

• El electrón… of course• Medición de la relación carga a masa

• Descubierto por J. J. Thomson

3-1 Quantization of Electric Charge 121

the particles were undeflected. This allowed him to determine the speed of the elec-trons by equating the magnitudes of the magnetic and electric forces and then to com-pute e�m(��q�m) from Equation 3-2:

quB � q� or u ��

B 3-3

Thomson’s experiment was remarkable in that he measured e�m for a subatomic par-ticle using only a voltmeter, an ammeter, and a measuring rod, obtaining the result 0.7 � 1011 C/kg. Present-day particle physicists routinely use the modern equivalent of Thomson’s experiment to measure the momenta of elementary particles.

Thomson repeated the experiment with different gases in the tube and different met-als for cathodes and always obtained the same value for e�m within his experimental

Thomson’s technique for controlling the direction of the electron beam with “crossed” electric and magnetic fields was subsequently applied in the development of cathode-ray tubes used in oscilloscopes and the picture tubes of older television receivers.

C A B

D

E–

+

FIGURE 3-1 J. J. Thomson’s tube for measuring e�m. Electrons from the cathode C pass through the slits at A and B and strike a phosphorescent screen. The beam can be deflected by an electric field between the plates D and E or by a magnetic field (not shown) whose direction is perpendicular to the electric field between D and E. From the deflections measured on a scale on the tube at the screen, e�m can be determined. [From J. J. Thomson, “Cathode Rays,” Philosophical Magazine (5), 44, 293 (1897).]

J. J. Thomson in his laboratory. He is facing the screen end of an e�m tube; an older cathode-ray tube is visible in front of his left shoulder. [Courtesy of Cavendish Laboratory.]

TIPLER_03_119-152hr2.indd 121 8/22/11 11:33 AM

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Radiación térmica:Evidencia experimental

• 1879: Ley de Stefan-Boltzmann,

• 1893: Ley de desplazamiento de Wien,

124 Chapter 3 Quantization of Charge, Light, and Energy

that the body glows and becomes a dull red. At higher temperatures it becomes bright red or even “white hot.”

A body that absorbs all radiation incident on it is called an ideal blackbody. In 1879 Josef Stefan found an empirical relation between the power radiated by an ideal blackbody and the temperature: R � ST 4 3-4where R is the power radiated per unit area, T is the absolute temperature, and S � 5.6703 � 10�8 W/m2K4 is a constant called Stefan’s constant. This result was also derived on the basis of classical thermodynamics by Ludwig Boltzmann about five years later, and Equation 3-4 is now called the Stefan-Boltzmann law. Note that the power per unit area radiated by a blackbody depends only on the temperature and not on any other characteristic of the object, such as its color or the material of which it is composed. Note, too, that R tells us the rate at which energy is emitted by the object. For example, doubling the absolute temperature of an object, for example, a star, increases the energy flow out of the object by a factor of 24 � 16. An object at room temperature (300°C) will double the rate at which it radiates energy as a result of a temperature increase of only 57°C. Thus, the Stefan-Boltzmann law has an enor-mous effect on the establishment of thermal equilibrium in physical systems.

Objects that are not ideal blackbodies radiate energy per unit area at a rate less than that of a blackbody at the same temperature. For those objects the rate does depend on properties in addition to the temperature, such as color and the composition of the surface. The effects of those dependencies are combined into a factor called the emissivity E, which multiplies the right side of Equation 3-4. The values of E, which is itself temperature dependent, are always less than unity.

Like the total radiated power R, the spectral distribution of the radiation emitted by a blackbody is found empirically to depend only on the absolute temperature T. The spectral distribution is determined experimentally as illustrated schematically in Figure 3-3. With R(L) d L the power emitted per unit area with wavelength between L and L � d L, Figure 3-4 shows the measured spectral distribution function R(L) versus L for several values of T ranging from 1000 K to 6000 K.

The R(L) curves in Figure 3-4 are quite remarkable in several respects. One is that the wavelength at which the distribution has its maximum value varies inversely with the temperature:

Lm ^1T

or

Lm T � constant � 2.898 � 10�3 m � K 3-5

FIGURE 3-3 Radiation emitted by the object at temperature T that passes through the slit is dispersed according to its wavelengths. The prism shown would be an appropriate device for that part of the emitted radiation in the visible region. In other spectral regions other types of devices or wavelength-sensitive detectors would be used.

Detector

Dispersedradiation

Object

SlitPrism

T

Radiation

TIPLER_03_119-152hr2.indd 124 8/22/11 11:33 AM

3-2 Blackbody Radiation 125

This result is known as Wien’s displacement law. It was obtained by Wien in 1893. Examples 3-1 and 3-2 illustrate its application.

EXAMPLE 3-1 How Big Is a Star? Measurement of the wavelength at which the spectral distribution R(L) from a certain star is maximum indicates that the star’s surface temperature is 3000 K. If the star is also found to radiate 100 times the power P^ radiated by the Sun, how big is the star? (The symbol ^ � Sun.) The Sun’s surface temperature is 5800 K.

SOLUTIONAssuming the Sun and the star both radiate as blackbodies (astronomers nearly always make that assumption, based on, among other things, the fact that the solar spectrum is very nearly that of an ideal blackbody), their surface temperatures have been determined from Equation 3-5 to be 5800 K and 3000 K, respectively. Mea-surement also indicates that Pstar � 100 P^. Thus, from Equation 3-4 we have that

Rstar �Pstar

(area)star�

100 P^

4Pr 2star

� ST 4star

and

R^ �P^

(area)^�

P^

4Pr 2^� ST 4

^

Thus, we have

r 2star � 100 r 2

^ 4 T^

Tstar5 4

rstar � 10 r^ 4 T^

Tstar5 2

� 104 58003000

5 2

r^

rstar � 37.4 r^Since r^ � 6.96 � 108 m, this star has a radius of about 2.6 � 1010 m, or about half the radius of the orbit of Mercury. This star is a red giant (see Chapter 13).

FIGURE 3-4 Spectral distribution function R(L) measured at different temperatures. The R(L) axis is in arbitrary units for comparison only. Notice the range of L in the visible spectrum. The Sun emits radiation very close to that of a blackbody at 5800 K. Lm is indicated for the 5000 K and 6000 K curves.

0.3

0.2

0

0.1

0 500

Visible6000 K

4000 K3000 K

1000Wavelength L (nm)

1500 2000

R(L

)

5000 K

Lm

Lm

0.001

00

2000 K

1500 K

1000 K

2000 4000L (nm)

R(L

)

TIPLER_03_119-152hr2.indd 125 8/22/11 11:33 AM

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Radiación térmica:Cuerpo negro y resultados clásicos

• Distribución de Rayleigh-Jeans


Rayleigh-Jeans EquationThe calculation of the distribution function R(L) involves the calculation of the energy density of electromagnetic waves in a cavity. Materials such as black velvet or lampblack come close to being ideal blackbodies, but the best practical realiza-tion of a ideal blackbody is a small hole leading into a cavity (such as a keyhole in a closet door; see Figure 3-5). Radiation incident on the hole has little chance of being reflected back out of the hole before it is absorbed by the walls of the cavity. The power radiated out of the hole is proportional to the total energy density U (the energy per unit volume of the radiation in the cavity). The proportionality constant can be shown to be c�4, where c is the speed of light.8

R �14

cU 3-6

Similarly, the spectral distribution of the power emitted from the hole is proportional to the spectral distribution of the energy density in the cavity. If u(L) d L is the frac-tion of the energy per unit volume in the cavity in the range d L, then u(L) and R(L) are related by

R(L) �14

cu(L) 3-7

The energy density distribution function u(L) can be calculated from classical physics in a straightforward way. The method involves finding the number of modes of oscillation of the electromagnetic field in the cavity with wavelengths in the inter-val d L and multiplying by the average energy per mode. The result is that the number of modes of oscillation per unit volume, n(L), is independent of the shape of the cav-ity and is given by

n(L) � 8PL�4 3-8

According to classical kinetic theory, the average energy per mode of oscillation is kT, the same as for a one-dimensional harmonic oscillator, where k is the Boltzmann constant. Classical theory thus predicts for the energy density distribution function

u�L� � kT n�L� � 8PkT L�4 3-9

This prediction, initially derived by Lord Rayleigh,9 is called the Rayleigh-Jeans equation. It is illustrated in Figure 3-6.

At very long wavelengths the Rayleigh-Jeans equation agrees with the experi-mentally determined spectral distribution, but at short wavelengths this equation pre-dicts that u(L) becomes large, approaching infinity as L 4 0, whereas experiment shows (see Figure 3-4) that the distribution actually approaches zero as L 4 0. This enormous disagreement between the experimental measurement of u(L) and the pre-diction of the fundamental laws of classical physics at short wavelengths was called the ultraviolet catastrophe. The word catastrophe was not used lightly; Equation 3-9 implies that

)R

0u�L� d L 4 @ 3-10

That is, every object would have an infinite energy density, which observation assures us is not true.

CCR

FIGURE 3-5 A small hole in the wall of a cavity approximating an ideal blackbody. Radiation entering the hole has little chance of leaving before it is completely absorbed within the cavity.

16

TIPLER_03_119-152hr4.indd 126 9/8/11 11:18 AM

• Distribución de Wien

u⌫ =8⇡kT

c3⌫2

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u⌫(Wien) ⇠8⇡⌫3

c3e�↵⌫/kT

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Radiación térmica:Hipótesis de Planck y consecuencias• Hipótesis de M. Planck:

• La radiación EM posee energías discretas en unidades enteras de una cantidad mínima y sólo depende de su frecuencia

• Distribución de energía

E = nh⌫<latexit sha1_base64="InvRSE1kTfka5Y76l+HUhJimomc=">AAAB6HicbZDNSsNAFIVv/K31r+rSzWARXJVEBN0IRRFcVrA/0IYymd40YyeTMDMRSug76ErUnc/jC/g2TmsW2npW39xzBu65QSq4Nq775Swtr6yurZc2yptb2zu7lb39lk4yxbDJEpGoTkA1Ci6xabgR2EkV0jgQ2A5G11O//YhK80Tem3GKfkyHkoecUWNH7ZtLGfVk1q9U3Zo7E1kEr4AqFGr0K5+9QcKyGKVhgmrd9dzU+DlVhjOBk3Iv05hSNqJD7FqUNEbt57N1J+Q4TBQxEZLZ+3c2p7HW4ziwmZiaSM970+F/Xjcz4YWfc5lmBiWzEeuFmSAmIdPWZMAVMiPGFihT3G5JWEQVZcbepmzre/NlF6F1WvPcmnd3Vq1fFYcowSEcwQl4cA51uIUGNIHBCJ7hDd6dB+fJeXFef6JLTvHnAP7I+fgG6e6M7A==</latexit><latexit sha1_base64="InvRSE1kTfka5Y76l+HUhJimomc=">AAAB6HicbZDNSsNAFIVv/K31r+rSzWARXJVEBN0IRRFcVrA/0IYymd40YyeTMDMRSug76ErUnc/jC/g2TmsW2npW39xzBu65QSq4Nq775Swtr6yurZc2yptb2zu7lb39lk4yxbDJEpGoTkA1Ci6xabgR2EkV0jgQ2A5G11O//YhK80Tem3GKfkyHkoecUWNH7ZtLGfVk1q9U3Zo7E1kEr4AqFGr0K5+9QcKyGKVhgmrd9dzU+DlVhjOBk3Iv05hSNqJD7FqUNEbt57N1J+Q4TBQxEZLZ+3c2p7HW4ziwmZiaSM970+F/Xjcz4YWfc5lmBiWzEeuFmSAmIdPWZMAVMiPGFihT3G5JWEQVZcbepmzre/NlF6F1WvPcmnd3Vq1fFYcowSEcwQl4cA51uIUGNIHBCJ7hDd6dB+fJeXFef6JLTvHnAP7I+fgG6e6M7A==</latexit><latexit sha1_base64="InvRSE1kTfka5Y76l+HUhJimomc=">AAAB6HicbZDNSsNAFIVv/K31r+rSzWARXJVEBN0IRRFcVrA/0IYymd40YyeTMDMRSug76ErUnc/jC/g2TmsW2npW39xzBu65QSq4Nq775Swtr6yurZc2yptb2zu7lb39lk4yxbDJEpGoTkA1Ci6xabgR2EkV0jgQ2A5G11O//YhK80Tem3GKfkyHkoecUWNH7ZtLGfVk1q9U3Zo7E1kEr4AqFGr0K5+9QcKyGKVhgmrd9dzU+DlVhjOBk3Iv05hSNqJD7FqUNEbt57N1J+Q4TBQxEZLZ+3c2p7HW4ziwmZiaSM970+F/Xjcz4YWfc5lmBiWzEeuFmSAmIdPWZMAVMiPGFihT3G5JWEQVZcbepmzre/NlF6F1WvPcmnd3Vq1fFYcowSEcwQl4cA51uIUGNIHBCJ7hDd6dB+fJeXFef6JLTvHnAP7I+fgG6e6M7A==</latexit><latexit sha1_base64="InvRSE1kTfka5Y76l+HUhJimomc=">AAAB6HicbZDNSsNAFIVv/K31r+rSzWARXJVEBN0IRRFcVrA/0IYymd40YyeTMDMRSug76ErUnc/jC/g2TmsW2npW39xzBu65QSq4Nq775Swtr6yurZc2yptb2zu7lb39lk4yxbDJEpGoTkA1Ci6xabgR2EkV0jgQ2A5G11O//YhK80Tem3GKfkyHkoecUWNH7ZtLGfVk1q9U3Zo7E1kEr4AqFGr0K5+9QcKyGKVhgmrd9dzU+DlVhjOBk3Iv05hSNqJD7FqUNEbt57N1J+Q4TBQxEZLZ+3c2p7HW4ziwmZiaSM970+F/Xjcz4YWfc5lmBiWzEeuFmSAmIdPWZMAVMiPGFihT3G5JWEQVZcbepmzre/NlF6F1WvPcmnd3Vq1fFYcowSEcwQl4cA51uIUGNIHBCJ7hDd6dB+fJeXFef6JLTvHnAP7I+fgG6e6M7A==</latexit>

u⌫ =8⇡h⌫3

c31

eh⌫/kT � 1<latexit sha1_base64="hUyjq8Jytk5syXKLCgig56w/KaE=">AAACF3icbVDLSgMxFM3UV62vqks3wSK4sc5owW6EohuXFfqCzrRk0jttaOZBkhHKMB+iP6MrUXHj0r8xbWehrWcRzj3nXMg9bsSZVKb5beRWVtfWN/Kbha3tnd294v5BS4axoNCkIQ9FxyUSOAugqZji0IkEEN/l0HbHt1O//QBCsjBoqEkEjk+GAfMYJUpL/WIl7ttBfG17gtCkakcMj/Tcu0wTqp+5bKUJ9JKpfj5upGdW2i+WzLI5A14mVkZKKEO9X/y0ByGNfQgU5UTKrmVGykmIUIxySAt2LCEidEyG0NU0ID5IJ5ldl+ITLxRYjQDP5t/ZhPhSTnxXZ3yiRnLRm4r/ed1YeVUnYUEUKwiojmjPizlWIZ6WhAdMAFV8ogmhgulfYjoiugulqyzo863FY5dJ66JsmWXrvlKq3WRF5NEROkanyEJXqIbuUB01EUVP6AW9ow/j0Xg2Xo23eTRnZDuH6A+Mrx9utqAA</latexit><latexit sha1_base64="hUyjq8Jytk5syXKLCgig56w/KaE=">AAACF3icbVDLSgMxFM3UV62vqks3wSK4sc5owW6EohuXFfqCzrRk0jttaOZBkhHKMB+iP6MrUXHj0r8xbWehrWcRzj3nXMg9bsSZVKb5beRWVtfWN/Kbha3tnd294v5BS4axoNCkIQ9FxyUSOAugqZji0IkEEN/l0HbHt1O//QBCsjBoqEkEjk+GAfMYJUpL/WIl7ttBfG17gtCkakcMj/Tcu0wTqp+5bKUJ9JKpfj5upGdW2i+WzLI5A14mVkZKKEO9X/y0ByGNfQgU5UTKrmVGykmIUIxySAt2LCEidEyG0NU0ID5IJ5ldl+ITLxRYjQDP5t/ZhPhSTnxXZ3yiRnLRm4r/ed1YeVUnYUEUKwiojmjPizlWIZ6WhAdMAFV8ogmhgulfYjoiugulqyzo863FY5dJ66JsmWXrvlKq3WRF5NEROkanyEJXqIbuUB01EUVP6AW9ow/j0Xg2Xo23eTRnZDuH6A+Mrx9utqAA</latexit><latexit sha1_base64="hUyjq8Jytk5syXKLCgig56w/KaE=">AAACF3icbVDLSgMxFM3UV62vqks3wSK4sc5owW6EohuXFfqCzrRk0jttaOZBkhHKMB+iP6MrUXHj0r8xbWehrWcRzj3nXMg9bsSZVKb5beRWVtfWN/Kbha3tnd294v5BS4axoNCkIQ9FxyUSOAugqZji0IkEEN/l0HbHt1O//QBCsjBoqEkEjk+GAfMYJUpL/WIl7ttBfG17gtCkakcMj/Tcu0wTqp+5bKUJ9JKpfj5upGdW2i+WzLI5A14mVkZKKEO9X/y0ByGNfQgU5UTKrmVGykmIUIxySAt2LCEidEyG0NU0ID5IJ5ldl+ITLxRYjQDP5t/ZhPhSTnxXZ3yiRnLRm4r/ed1YeVUnYUEUKwiojmjPizlWIZ6WhAdMAFV8ogmhgulfYjoiugulqyzo863FY5dJ66JsmWXrvlKq3WRF5NEROkanyEJXqIbuUB01EUVP6AW9ow/j0Xg2Xo23eTRnZDuH6A+Mrx9utqAA</latexit><latexit sha1_base64="hUyjq8Jytk5syXKLCgig56w/KaE=">AAACF3icbVDLSgMxFM3UV62vqks3wSK4sc5owW6EohuXFfqCzrRk0jttaOZBkhHKMB+iP6MrUXHj0r8xbWehrWcRzj3nXMg9bsSZVKb5beRWVtfWN/Kbha3tnd294v5BS4axoNCkIQ9FxyUSOAugqZji0IkEEN/l0HbHt1O//QBCsjBoqEkEjk+GAfMYJUpL/WIl7ttBfG17gtCkakcMj/Tcu0wTqp+5bKUJ9JKpfj5upGdW2i+WzLI5A14mVkZKKEO9X/y0ByGNfQgU5UTKrmVGykmIUIxySAt2LCEidEyG0NU0ID5IJ5ldl+ITLxRYjQDP5t/ZhPhSTnxXZ3yiRnLRm4r/ed1YeVUnYUEUKwiojmjPizlWIZ6WhAdMAFV8ogmhgulfYjoiugulqyzo863FY5dJ66JsmWXrvlKq3WRF5NEROkanyEJXqIbuUB01EUVP6AW9ow/j0Xg2Xo23eTRnZDuH6A+Mrx9utqAA</latexit>

R =

Z 1

0u⌫d⌫ =

2⇡5k4

15c2h3T 4

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� =2⇡5k4

15c2h3= 5.67⇥ 10�8 W/m2K4

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Constante de Stefan

Efecto fotoeléctrico


and interrupted his other work for six months in order to study it in detail. His results, published later that year, were then extended by others. It was found that negative particles were emitted from a clean surface when exposed to light. P. Lenard in 1900 deflected them in a magnetic field and found that they had a charge-to-mass ratio of the same magnitude as that measured by Thomson for cathode rays: the particles being emitted were electrons.

Figure 3-8 shows a schematic diagram of the basic apparatus used by Lenard. When light L is incident on a clean metal surface (cathode C ), electrons are emitted. If some of these electrons that reach the anode A pass through the small hole, a current results in the external electrometer circuit connected to A. The number of the emitted electrons reaching the anode can be increased or decreased by making the anode positive or nega-tive with respect to the cathode. Letting V be the potential difference between the cath-ode and anode, Figure 3-9a shows the current versus V for two values of the intensity of light incident on the cathode. When V is positive, the electrons are attracted to the anode. At sufficiently large V all the emitted electrons reach the anode and the current reaches its maximum value. Lenard observed that the maximum current was propor-tional to the light intensity, an expected result since doubling the energy per unit time incident on the cathode should double the number of electrons emitted. Intensities too low to provide the electrons with the energy necessary to escape from the metal should result in no emission of electrons. However, in contrast with the classical expectation, there was no minimum intensity below which the current was absent. When V is nega-tive, the electrons are repelled from the anode. Then, only electrons with initial kinetic energy mv2�2 greater than e|V | can reach the anode. From Figure 3-9a we see that if V is less than �V0, no electrons reach the anode. The potential V0 is called the stopping potential. It is related to the maximum kinetic energy of the emitted electrons by

4 12

mv25 � eV0 3-20

The experimental result, illustrated by Figure 3-9a, that V0 is independent of the incident light intensity was surprising. Apparently, increasing the rate of energy falling on the cathode does not increase the maximum kinetic energy of the emitted electrons, con-trary to classical expectations. In 1905, Einstein offered an explanation of this result

A

��

W

V

B

L

W

C

Pump

FIGURE 3-8 Schematic diagram of the apparatus used by P. Lenard to demonstrate the photoelectric effect and to show that the particles emitted in the process were electrons. Light from the source L strikes the cathode C. Photoelectrons going through the hole in anode A are recorded by the electrometer connected to A. A magnetic field, indicated by the circular pole piece, could deflect the particles to a second electrometer connected to B, making possible the establishment of the sign of the charges and their e�m ratio. [P. Lenard, Annalen der Physik, 2, 359 (1900).]

TIPLER_03_119-152hr2.indd 132 8/22/11 11:33 AM

eV = K = h⌫ � �<latexit sha1_base64="+66WBZx48PyHBsqv5kn57/4u+9E=">AAAB73icbZDLSsNAFIZP6q3WW9Wlm8EiuLEkIuimUHQjuKlgL9DEMpmeNEMnF2cmQgl9Dl2JuvNdfAHfxmntQlv/1Tfn/wfOf/xUcKVt+8sqLC2vrK4V10sbm1vbO+XdvZZKMsmwyRKRyI5PFQoeY1NzLbCTSqSRL7DtD68mfvsRpeJJfKdHKXoRHcQ84IxqM7rHVu2mFrpxduKmIe+VK3bVnoosgjODCszU6JU/3X7CsghjzQRVquvYqfZyKjVnAsclN1OYUjakA+wajGmEysunW4/JUZBIokMk0/fvbE4jpUaRbzIR1aGa9ybD/7xupoMLL+dxmmmMmYkYL8gE0QmZlCd9LpFpMTJAmeRmS8JCKinT5kQlU9+ZL7sIrdOqY1ed27NK/XJ2iCIcwCEcgwPnUIdraEATGEh4hjd4tx6sJ+vFev2JFqzZn334I+vjG4a8j4w=</latexit><latexit sha1_base64="+66WBZx48PyHBsqv5kn57/4u+9E=">AAAB73icbZDLSsNAFIZP6q3WW9Wlm8EiuLEkIuimUHQjuKlgL9DEMpmeNEMnF2cmQgl9Dl2JuvNdfAHfxmntQlv/1Tfn/wfOf/xUcKVt+8sqLC2vrK4V10sbm1vbO+XdvZZKMsmwyRKRyI5PFQoeY1NzLbCTSqSRL7DtD68mfvsRpeJJfKdHKXoRHcQ84IxqM7rHVu2mFrpxduKmIe+VK3bVnoosgjODCszU6JU/3X7CsghjzQRVquvYqfZyKjVnAsclN1OYUjakA+wajGmEysunW4/JUZBIokMk0/fvbE4jpUaRbzIR1aGa9ybD/7xupoMLL+dxmmmMmYkYL8gE0QmZlCd9LpFpMTJAmeRmS8JCKinT5kQlU9+ZL7sIrdOqY1ed27NK/XJ2iCIcwCEcgwPnUIdraEATGEh4hjd4tx6sJ+vFev2JFqzZn334I+vjG4a8j4w=</latexit><latexit sha1_base64="+66WBZx48PyHBsqv5kn57/4u+9E=">AAAB73icbZDLSsNAFIZP6q3WW9Wlm8EiuLEkIuimUHQjuKlgL9DEMpmeNEMnF2cmQgl9Dl2JuvNdfAHfxmntQlv/1Tfn/wfOf/xUcKVt+8sqLC2vrK4V10sbm1vbO+XdvZZKMsmwyRKRyI5PFQoeY1NzLbCTSqSRL7DtD68mfvsRpeJJfKdHKXoRHcQ84IxqM7rHVu2mFrpxduKmIe+VK3bVnoosgjODCszU6JU/3X7CsghjzQRVquvYqfZyKjVnAsclN1OYUjakA+wajGmEysunW4/JUZBIokMk0/fvbE4jpUaRbzIR1aGa9ybD/7xupoMLL+dxmmmMmYkYL8gE0QmZlCd9LpFpMTJAmeRmS8JCKinT5kQlU9+ZL7sIrdOqY1ed27NK/XJ2iCIcwCEcgwPnUIdraEATGEh4hjd4tx6sJ+vFev2JFqzZn334I+vjG4a8j4w=</latexit><latexit sha1_base64="+66WBZx48PyHBsqv5kn57/4u+9E=">AAAB73icbZDLSsNAFIZP6q3WW9Wlm8EiuLEkIuimUHQjuKlgL9DEMpmeNEMnF2cmQgl9Dl2JuvNdfAHfxmntQlv/1Tfn/wfOf/xUcKVt+8sqLC2vrK4V10sbm1vbO+XdvZZKMsmwyRKRyI5PFQoeY1NzLbCTSqSRL7DtD68mfvsRpeJJfKdHKXoRHcQ84IxqM7rHVu2mFrpxduKmIe+VK3bVnoosgjODCszU6JU/3X7CsghjzQRVquvYqfZyKjVnAsclN1OYUjakA+wajGmEysunW4/JUZBIokMk0/fvbE4jpUaRbzIR1aGa9ybD/7xupoMLL+dxmmmMmYkYL8gE0QmZlCd9LpFpMTJAmeRmS8JCKinT5kQlU9+ZL7sIrdOqY1ed27NK/XJ2iCIcwCEcgwPnUIdraEATGEh4hjd4tx6sJ+vFev2JFqzZn334I+vjG4a8j4w=</latexit>


the stopping potential V0 on the frequency. Careful experiments by Millikan, reported in 1914 and in more detail in 1916, showed that Equation 3-21 was correct and that measurements of h from it agreed with the value obtained by Planck. A plot taken from this work is shown in Figure 3-10.

The minimum, or threshold, frequency for photoelectric effect, labeled ft in this plot and in Figure 3-9b, and the corresponding threshold wavelength Lt are related to the work function F by setting V0 � 0 in Equation 3-21:

F � hft �hcLt

3-22

Photons of frequencies lower than ft (and therefore having wavelengths greater than Lt) do not have enough energy to eject an electron from the metal. Work functions for metals are typically on the order of a few electron volts. The work functions for sev-eral elements are given in Table 3-1.

FIGURE 3-10 Millikan’s data for stopping potential versus frequency for the photoelectric effect. The data fall on a straight line with slope h�e, as predicted by Einstein a decade before the experiment. The intercept on the stopping potential axis is �F�e. [R. A. Millikan, Physical Review, 7, 362 (1915).]

Table 3-1 Photoelectric work functions

Element Work function (eV)

Na 2.28

Cs 1.95

Cd 4.07

Al 4.08

Ag 4.73

Pt 6.35

Mg 3.68

Ni 5.01

Se 5.11

Pb 4.14

Stop

ping

pot

entia

l (V 0

)

3

2

1

0

–1

40 50 60 70 80

Frequency ( � 1013 Hz)

90 100 110 120 � 1013

ft = 43.9 � 1013

TIPLER_03_119-152hr2.indd 134 8/22/11 11:33 AM

• 1905, A. Einstein

La energía cinética del electrón depende linealmente de la frecuencia de la luz incidente, la cual está constituida por elementos discretos llamados cuantos de radiación EM, o fotones

Rayos X


X RaysThe German physicist Wilhelm K. Roentgen discovered x rays in 1895 when he was working with a cathode-ray tube. Coming five years before Planck’s explanation of the blackbody emission spectrum, Roentgen’s discovery turned out to be the first significant development in quantum physics. He found that “rays” originating from the point where the cathode rays (electrons) hit the glass tube, or a target within the tube, could pass through materials opaque to light and activate a fluorescent screen or photographic film. He investigated this phenomenon extensively and found that all materials were transparent to these rays to some degree and that the transparency decreased with increasing density. This fact led to the medical use of x rays within months after the publication of Roentgen’s first paper.14

Roentgen was unable to deflect these rays in a magnetic field, nor was he able to observe refraction or the interference phenomena associated with waves. He thus gave the rays the somewhat mysterious name of x rays. Since classical electromag-netic theory predicts that accelerated charges will radiate electromagnetic waves, it is natural to expect that x rays are electromagnetic waves produced by the acceleration of the electrons when they are deflected and stopped by the atoms of a target. Such radiation is called bremsstrahlung, German for “braking radiation.” The slight dif-fraction broadening of an x-ray beam after passing through slits a few thousandths of a millimeter wide indicated their wavelengths to be of the order of 10�10 m � 0.1 nm. In 1912, Laue suggested that since the wavelengths of x rays were of the same order

(a) Early x-ray tube. [Courtesy of Cavendish Laboratory.](b) x-ray tubes became more compact over time. This tube was a design typical of the mid-twentieth century. [Courtesy of Schenectady Museum, Hall of Electrical History, Schenectady, NY.](c) Diagram of the components of a modern x-ray tube. Design technology has advanced enormously, making possible very high operating voltages, beam currents, and x-ray intensities, but essential elements of the tubes remain unchanged.

(a) (b)

Tungstentarget

Anode Cathode

Pyrex glassenvelope Electron

beamFilament

X rays

+ –

(c)

TIPLER_03_119-152hr2.indd 138 8/22/11 11:33 AM





(a) (b)

Tungstentarget

Anode Cathode


beamFilament

X rays

+ –

(c)

TIPLER_03_119-152hr2.indd 138 8/22/11 11:33 AM





(a) (b)

Tungstentarget

Anode Cathode


beamFilament

X rays

+ –

(c)

TIPLER_03_119-152hr2.indd 138 8/22/11 11:33 AM

• 1895, Wilhelm Roentgen

Dispersión Compton:Evidencia experimental


function of the scattering angle U. The result, called Compton’s equation and derived in a More section on the home page, is

L2 � L1 �h

mc �1 � cos U� 3-25

The change in wavelength is thus predicted to be independent of the original wavelength. The quantity h�mc has the dimensions of length and is called the Compton wave-length of the electron. Its value is

Lc �h

mc �hc

mc2 �1.24 � 103 eV � nm

5.11 � 105 eV� 0.00243 nm

Because L2 � L1 is small, it is difficult to observe unless L1 is very small so that the fractional change (L2 � L1)�L1 is appreciable. For this reason Compton effect is gen-erally only observed for x rays and gamma radiation.

Compton verified his result experimentally using the characteristic x-ray line of wavelength 0.0711 nm from molybdenum for the incident monochromatic photons and scattering these photons from electrons in graphite. The wavelength of the scat-tered photons was measured using a Bragg crystal spectrometer. His experimental arrangement is shown in Figure 3-16; Figure 3-17 shows his results. The first peak at each scattering angle corresponds to scattering with no shift in the wavelength due to scattering by the inner electrons of carbon. Since these are tightly bound to the atom, it is the entire atom that recoils rather than the individual electrons. The expected shift in this case is given by Equation 3-25, with m being the mass of the atom, which is about 104 times that of the electron; thus, this shift is negligible. The variation of$L � L2 � L1 with U was found to that predicted by Equation 3-25.

We have seen in this and the preceding two sections that the interaction of elec-tromagnetic radiation with matter is a discrete interaction that occurs at the atomic level. It is perhaps curious that after so many years of debate about the nature of light, we now find that we must have both a particle (i.e., quantum) theory to describe in detail the energy exchange between electromagnetic radiation and mat-ter and a wave theory to describe the interference and diffraction of electromag-netic radiation. We will discuss this so-called wave-particle duality in more detail in Chapter 5.

F

X-ray tube(Mo target)

RS1

DefiningslitS2

Calcitecrystal

Braggspectrometer

Ionizationchamber

Shutter

FIGURE 3-16 Schematic sketch of Compton’s apparatus. x rays from the tube strike the carbon block R and are scattered into a Bragg-type crystal spectrometer. In this diagram, the scattering angle is 30°. The beam was defined by slits S1 and S2. Although the entire spectrum is being scattered by R, the spectrometer scanned the region around the KA line of molybdenum.

FIGURE 3-17 Intensity versus wavelength for Compton scattering at several angles. The left peak in each case results from photons of the original wavelength that are scattered by tightly bound electrons, which have an effective mass equal to that of the atom. The separation in wavelength of the peaks is given by Equation 3-25. The horizontal scale used by Compton “angle from calcite” refers to the calcite analyzing crystal in Figure 3-16.

(a)

(c)

Scatteredat 90°

(b)

(d )

135°

MolybdenumKα lineprimary

Scattered bygraphite at45°

6°30� 7°30�7°Angle from calcite

TIPLER_03_119-152hr2.indd 142 8/22/11 11:33 AM



L2 � L1 �h

mc �1 � cos U� 3-25


Lc �h

mc �hc

mc2 �1.24 � 103 eV � nm

5.11 � 105 eV� 0.00243 nm




F


RS1

DefiningslitS2

Calcitecrystal

Braggspectrometer

Ionizationchamber

Shutter



(a)

(c)

Scatteredat 90°

(b)

(d )

135°




TIPLER_03_119-152hr2.indd 142 8/22/11 11:33 AM



L2 � L1 �h

mc �1 � cos U� 3-25


Lc �h

mc �hc

mc2 �1.24 � 103 eV � nm

5.11 � 105 eV� 0.00243 nm




F


RS1

DefiningslitS2

Calcitecrystal

Braggspectrometer

Ionizationchamber

Shutter



(a)

(c)

Scatteredat 90°

(b)

(d )

135°




TIPLER_03_119-152hr2.indd 142 8/22/11 11:33 AM



L2 � L1 �h

mc �1 � cos U� 3-25


Lc �h

mc �hc

mc2 �1.24 � 103 eV � nm

5.11 � 105 eV� 0.00243 nm




F


RS1

DefiningslitS2

Calcitecrystal

Braggspectrometer

Ionizationchamber

Shutter



(a)

(c)

Scatteredat 90°

(b)

(d )

135°




TIPLER_03_119-152hr2.indd 142 8/22/11 11:33 AM



L2 � L1 �h

mc �1 � cos U� 3-25


Lc �h

mc �hc

mc2 �1.24 � 103 eV � nm

5.11 � 105 eV� 0.00243 nm




F


RS1

DefiningslitS2

Calcitecrystal

Braggspectrometer

Ionizationchamber

Shutter



(a)

(c)

Scatteredat 90°

(b)

(d )

135°




TIPLER_03_119-152hr2.indd 142 8/22/11 11:33 AM

Efecto Compton:Descripción corpuscular de la luz

�0 � � =h

mec(1� cos ✓)

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Ee = mec2

<latexit sha1_base64="7Z3+ex7gck1G22cUW+mwGIbt/RM=">AAAB63icbZDNSgMxFIXv+FvrX9Wlm2ARXJWZIuhGKIrgsoL9wXYcMultG5rMDElGKEOfQlei7nwbX8C3Ma2z0Naz+nLPCdxzw0RwbVz3y1laXlldWy9sFDe3tnd2S3v7TR2nimGDxSJW7ZBqFDzChuFGYDtRSGUosBWOrqZ+6xGV5nF0Z8YJ+pIOIt7njBo7ur8O8EIGyB6qQansVtyZyCJ4OZQhVz0ofXZ7MUslRoYJqnXHcxPjZ1QZzgROit1UY0LZiA6wYzGiErWfzTaekON+rIgZIpm9f2czKrUey9BmJDVDPe9Nh/95ndT0z/2MR0lqMGI2Yr1+KoiJybQ46XGFzIixBcoUt1sSNqSKMmPPU7T1vfmyi9CsVjy34t2elmuX+SEKcAhHcAIenEENbqAODWAQwTO8wbsjnSfnxXn9iS45+Z8D+CPn4xucS43d</latexit><latexit sha1_base64="7Z3+ex7gck1G22cUW+mwGIbt/RM=">AAAB63icbZDNSgMxFIXv+FvrX9Wlm2ARXJWZIuhGKIrgsoL9wXYcMultG5rMDElGKEOfQlei7nwbX8C3Ma2z0Naz+nLPCdxzw0RwbVz3y1laXlldWy9sFDe3tnd2S3v7TR2nimGDxSJW7ZBqFDzChuFGYDtRSGUosBWOrqZ+6xGV5nF0Z8YJ+pIOIt7njBo7ur8O8EIGyB6qQansVtyZyCJ4OZQhVz0ofXZ7MUslRoYJqnXHcxPjZ1QZzgROit1UY0LZiA6wYzGiErWfzTaekON+rIgZIpm9f2czKrUey9BmJDVDPe9Nh/95ndT0z/2MR0lqMGI2Yr1+KoiJybQ46XGFzIixBcoUt1sSNqSKMmPPU7T1vfmyi9CsVjy34t2elmuX+SEKcAhHcAIenEENbqAODWAQwTO8wbsjnSfnxXn9iS45+Z8D+CPn4xucS43d</latexit><latexit sha1_base64="7Z3+ex7gck1G22cUW+mwGIbt/RM=">AAAB63icbZDNSgMxFIXv+FvrX9Wlm2ARXJWZIuhGKIrgsoL9wXYcMultG5rMDElGKEOfQlei7nwbX8C3Ma2z0Naz+nLPCdxzw0RwbVz3y1laXlldWy9sFDe3tnd2S3v7TR2nimGDxSJW7ZBqFDzChuFGYDtRSGUosBWOrqZ+6xGV5nF0Z8YJ+pIOIt7njBo7ur8O8EIGyB6qQansVtyZyCJ4OZQhVz0ofXZ7MUslRoYJqnXHcxPjZ1QZzgROit1UY0LZiA6wYzGiErWfzTaekON+rIgZIpm9f2czKrUey9BmJDVDPe9Nh/95ndT0z/2MR0lqMGI2Yr1+KoiJybQ46XGFzIixBcoUt1sSNqSKMmPPU7T1vfmyi9CsVjy34t2elmuX+SEKcAhHcAIenEENbqAODWAQwTO8wbsjnSfnxXn9iS45+Z8D+CPn4xucS43d</latexit><latexit sha1_base64="7Z3+ex7gck1G22cUW+mwGIbt/RM=">AAAB63icbZDNSgMxFIXv+FvrX9Wlm2ARXJWZIuhGKIrgsoL9wXYcMultG5rMDElGKEOfQlei7nwbX8C3Ma2z0Naz+nLPCdxzw0RwbVz3y1laXlldWy9sFDe3tnd2S3v7TR2nimGDxSJW7ZBqFDzChuFGYDtRSGUosBWOrqZ+6xGV5nF0Z8YJ+pIOIt7njBo7ur8O8EIGyB6qQansVtyZyCJ4OZQhVz0ofXZ7MUslRoYJqnXHcxPjZ1QZzgROit1UY0LZiA6wYzGiErWfzTaekON+rIgZIpm9f2czKrUey9BmJDVDPe9Nh/95ndT0z/2MR0lqMGI2Yr1+KoiJybQ46XGFzIixBcoUt1sSNqSKMmPPU7T1vfmyi9CsVjy34t2elmuX+SEKcAhHcAIenEENbqAODWAQwTO8wbsjnSfnxXn9iS45+Z8D+CPn4xucS43d</latexit>

E = h⌫

p = E/c<latexit sha1_base64="WRyyUsogHa4O7vIM6XOeBWjLJZE=">AAAB9HicbZDLSsNAFIYn9VbrLdWlm8FicVUTEXRTKErBZQV7gSaUyfSkGTq5MDOplNA30ZWoO5/EF/BtnNYstPVffXP+f+Cc30s4k8qyvozC2vrG5lZxu7Szu7d/YJYPOzJOBYU2jXkseh6RwFkEbcUUh14igIQeh643vp373QkIyeLoQU0TcEMyipjPKFF6NDDLzWo9cKIUO04pqdab53RgVqyatRBeBTuHCsrVGpifzjCmaQiRopxI2betRLkZEYpRDrOSk0pICB2TEfQ1RiQE6WaL1Wf41I8FVgHgxft3NiOhlNPQ05mQqEAue/Phf14/Vf61m7EoSRVEVEe056ccqxjPG8BDJoAqPtVAqGB6S0wDIghVuqeSPt9ePnYVOhc126rZ95eVxk1eRBEdoxN0hmx0hRroDrVQG1H0iJ7RG3o3JsaT8WK8/kQLRv7nCP2R8fENVU6PxQ==</latexit><latexit sha1_base64="WRyyUsogHa4O7vIM6XOeBWjLJZE=">AAAB9HicbZDLSsNAFIYn9VbrLdWlm8FicVUTEXRTKErBZQV7gSaUyfSkGTq5MDOplNA30ZWoO5/EF/BtnNYstPVffXP+f+Cc30s4k8qyvozC2vrG5lZxu7Szu7d/YJYPOzJOBYU2jXkseh6RwFkEbcUUh14igIQeh643vp373QkIyeLoQU0TcEMyipjPKFF6NDDLzWo9cKIUO04pqdab53RgVqyatRBeBTuHCsrVGpifzjCmaQiRopxI2betRLkZEYpRDrOSk0pICB2TEfQ1RiQE6WaL1Wf41I8FVgHgxft3NiOhlNPQ05mQqEAue/Phf14/Vf61m7EoSRVEVEe056ccqxjPG8BDJoAqPtVAqGB6S0wDIghVuqeSPt9ePnYVOhc126rZ95eVxk1eRBEdoxN0hmx0hRroDrVQG1H0iJ7RG3o3JsaT8WK8/kQLRv7nCP2R8fENVU6PxQ==</latexit><latexit sha1_base64="WRyyUsogHa4O7vIM6XOeBWjLJZE=">AAAB9HicbZDLSsNAFIYn9VbrLdWlm8FicVUTEXRTKErBZQV7gSaUyfSkGTq5MDOplNA30ZWoO5/EF/BtnNYstPVffXP+f+Cc30s4k8qyvozC2vrG5lZxu7Szu7d/YJYPOzJOBYU2jXkseh6RwFkEbcUUh14igIQeh643vp373QkIyeLoQU0TcEMyipjPKFF6NDDLzWo9cKIUO04pqdab53RgVqyatRBeBTuHCsrVGpifzjCmaQiRopxI2betRLkZEYpRDrOSk0pICB2TEfQ1RiQE6WaL1Wf41I8FVgHgxft3NiOhlNPQ05mQqEAue/Phf14/Vf61m7EoSRVEVEe056ccqxjPG8BDJoAqPtVAqGB6S0wDIghVuqeSPt9ePnYVOhc126rZ95eVxk1eRBEdoxN0hmx0hRroDrVQG1H0iJ7RG3o3JsaT8WK8/kQLRv7nCP2R8fENVU6PxQ==</latexit><latexit sha1_base64="WRyyUsogHa4O7vIM6XOeBWjLJZE=">AAAB9HicbZDLSsNAFIYn9VbrLdWlm8FicVUTEXRTKErBZQV7gSaUyfSkGTq5MDOplNA30ZWoO5/EF/BtnNYstPVffXP+f+Cc30s4k8qyvozC2vrG5lZxu7Szu7d/YJYPOzJOBYU2jXkseh6RwFkEbcUUh14igIQeh643vp373QkIyeLoQU0TcEMyipjPKFF6NDDLzWo9cKIUO04pqdab53RgVqyatRBeBTuHCsrVGpifzjCmaQiRopxI2betRLkZEYpRDrOSk0pICB2TEfQ1RiQE6WaL1Wf41I8FVgHgxft3NiOhlNPQ05mQqEAue/Phf14/Vf61m7EoSRVEVEe056ccqxjPG8BDJoAqPtVAqGB6S0wDIghVuqeSPt9ePnYVOhc126rZ95eVxk1eRBEdoxN0hmx0hRroDrVQG1H0iJ7RG3o3JsaT8WK8/kQLRv7nCP2R8fENVU6PxQ==</latexit>

E0e2= m2

ec4 + p2ec

2, pe<latexit sha1_base64="iYIxJG2QCvrlFdAi7iFDUyVDmx8=">AAACGHicbZBLS8QwFIXT8T2+Rl26CQ6ioJS2KLoRRBFcjuDowDxKGm9tmKQtSSoMpX9E/4yuxMfKnf/GzGOhM97Vl3tOSM4JUs6UdpxvqzQ1PTM7N79QXlxaXlmtrK3fqCSTFOo04YlsBEQBZzHUNdMcGqkEIgIOt0H3vK/fPoBULImvdS+FtiD3MQsZJdqs/MphfrHjQ9HxToQPHY92DvbSIXj7uBWplFDIHds7pKLAeSsIcVr44Feqju0MBk+CO4IqGk3Nr3y27hKaCYg15USppuukup0TqRnlUJRbmQLzVJfcQ9NgTASodj6IV+DtMJFYR4AH59/enAileiIwHkF0pMa1/vI/rZnp8LidszjNNMTUWIwWZhzrBPdbwndMAtW8Z4BQycwvMY2IJFSbLssmvjsedhJuPNt1bPfqoHp6NipiHm2iLbSLXHSETtElqqE6ougJvaB39GE9Ws/Wq/U2tJas0Z0N9Gesrx96CZ4Y</latexit><latexit sha1_base64="iYIxJG2QCvrlFdAi7iFDUyVDmx8=">AAACGHicbZBLS8QwFIXT8T2+Rl26CQ6ioJS2KLoRRBFcjuDowDxKGm9tmKQtSSoMpX9E/4yuxMfKnf/GzGOhM97Vl3tOSM4JUs6UdpxvqzQ1PTM7N79QXlxaXlmtrK3fqCSTFOo04YlsBEQBZzHUNdMcGqkEIgIOt0H3vK/fPoBULImvdS+FtiD3MQsZJdqs/MphfrHjQ9HxToQPHY92DvbSIXj7uBWplFDIHds7pKLAeSsIcVr44Feqju0MBk+CO4IqGk3Nr3y27hKaCYg15USppuukup0TqRnlUJRbmQLzVJfcQ9NgTASodj6IV+DtMJFYR4AH59/enAileiIwHkF0pMa1/vI/rZnp8LidszjNNMTUWIwWZhzrBPdbwndMAtW8Z4BQycwvMY2IJFSbLssmvjsedhJuPNt1bPfqoHp6NipiHm2iLbSLXHSETtElqqE6ougJvaB39GE9Ws/Wq/U2tJas0Z0N9Gesrx96CZ4Y</latexit><latexit sha1_base64="iYIxJG2QCvrlFdAi7iFDUyVDmx8=">AAACGHicbZBLS8QwFIXT8T2+Rl26CQ6ioJS2KLoRRBFcjuDowDxKGm9tmKQtSSoMpX9E/4yuxMfKnf/GzGOhM97Vl3tOSM4JUs6UdpxvqzQ1PTM7N79QXlxaXlmtrK3fqCSTFOo04YlsBEQBZzHUNdMcGqkEIgIOt0H3vK/fPoBULImvdS+FtiD3MQsZJdqs/MphfrHjQ9HxToQPHY92DvbSIXj7uBWplFDIHds7pKLAeSsIcVr44Feqju0MBk+CO4IqGk3Nr3y27hKaCYg15USppuukup0TqRnlUJRbmQLzVJfcQ9NgTASodj6IV+DtMJFYR4AH59/enAileiIwHkF0pMa1/vI/rZnp8LidszjNNMTUWIwWZhzrBPdbwndMAtW8Z4BQycwvMY2IJFSbLssmvjsedhJuPNt1bPfqoHp6NipiHm2iLbSLXHSETtElqqE6ougJvaB39GE9Ws/Wq/U2tJas0Z0N9Gesrx96CZ4Y</latexit><latexit sha1_base64="iYIxJG2QCvrlFdAi7iFDUyVDmx8=">AAACGHicbZBLS8QwFIXT8T2+Rl26CQ6ioJS2KLoRRBFcjuDowDxKGm9tmKQtSSoMpX9E/4yuxMfKnf/GzGOhM97Vl3tOSM4JUs6UdpxvqzQ1PTM7N79QXlxaXlmtrK3fqCSTFOo04YlsBEQBZzHUNdMcGqkEIgIOt0H3vK/fPoBULImvdS+FtiD3MQsZJdqs/MphfrHjQ9HxToQPHY92DvbSIXj7uBWplFDIHds7pKLAeSsIcVr44Feqju0MBk+CO4IqGk3Nr3y27hKaCYg15USppuukup0TqRnlUJRbmQLzVJfcQ9NgTASodj6IV+DtMJFYR4AH59/enAileiIwHkF0pMa1/vI/rZnp8LidszjNNMTUWIwWZhzrBPdbwndMAtW8Z4BQycwvMY2IJFSbLssmvjsedhJuPNt1bPfqoHp6NipiHm2iLbSLXHSETtElqqE6ougJvaB39GE9Ws/Wq/U2tJas0Z0N9Gesrx96CZ4Y</latexit>

E0 = h⌫0

p0 = E0/c<latexit sha1_base64="1VwU09zYrtkQ/ZOTO0Qy+yGIBCA=">AAAB+HicbVDLSsNAFJ3UV42vqLhyM1i0rmoigm6EohRcVrAPaEKZTG+aoZMHMxOhhv6LrkTd+R3+gH/jtGah1bM6955z4dzjp5xJZdufRmlhcWl5pbxqrq1vbG5Z2zttmWSCQosmPBFdn0jgLIaWYopDNxVAIp9Dxx9dT/XOPQjJkvhOjVPwIjKMWcAoUXrVt/Ya1aPL0I2zKnZdM9VDo3pC+1bFrtkz4L/EKUgFFWj2rQ93kNAsglhRTqTsOXaqvJwIxSiHielmElJCR2QIPU1jEoH08ln8CT4MEoFVCHg2//TmJJJyHPnaExEVynltuvxP62UquPByFqeZgphqi9aCjGOV4GkLeMAEUMXHmhAqmE6JaUgEoUp3Zer3nfln/5L2ac2xa87tWaV+VRRRRvvoAB0jB52jOrpBTdRCFOXoCb2iN+PBeDSejZdva8kobnbRLxjvX+MUkIk=</latexit><latexit sha1_base64="1VwU09zYrtkQ/ZOTO0Qy+yGIBCA=">AAAB+HicbVDLSsNAFJ3UV42vqLhyM1i0rmoigm6EohRcVrAPaEKZTG+aoZMHMxOhhv6LrkTd+R3+gH/jtGah1bM6955z4dzjp5xJZdufRmlhcWl5pbxqrq1vbG5Z2zttmWSCQosmPBFdn0jgLIaWYopDNxVAIp9Dxx9dT/XOPQjJkvhOjVPwIjKMWcAoUXrVt/Ya1aPL0I2zKnZdM9VDo3pC+1bFrtkz4L/EKUgFFWj2rQ93kNAsglhRTqTsOXaqvJwIxSiHielmElJCR2QIPU1jEoH08ln8CT4MEoFVCHg2//TmJJJyHPnaExEVynltuvxP62UquPByFqeZgphqi9aCjGOV4GkLeMAEUMXHmhAqmE6JaUgEoUp3Zer3nfln/5L2ac2xa87tWaV+VRRRRvvoAB0jB52jOrpBTdRCFOXoCb2iN+PBeDSejZdva8kobnbRLxjvX+MUkIk=</latexit><latexit sha1_base64="1VwU09zYrtkQ/ZOTO0Qy+yGIBCA=">AAAB+HicbVDLSsNAFJ3UV42vqLhyM1i0rmoigm6EohRcVrAPaEKZTG+aoZMHMxOhhv6LrkTd+R3+gH/jtGah1bM6955z4dzjp5xJZdufRmlhcWl5pbxqrq1vbG5Z2zttmWSCQosmPBFdn0jgLIaWYopDNxVAIp9Dxx9dT/XOPQjJkvhOjVPwIjKMWcAoUXrVt/Ya1aPL0I2zKnZdM9VDo3pC+1bFrtkz4L/EKUgFFWj2rQ93kNAsglhRTqTsOXaqvJwIxSiHielmElJCR2QIPU1jEoH08ln8CT4MEoFVCHg2//TmJJJyHPnaExEVynltuvxP62UquPByFqeZgphqi9aCjGOV4GkLeMAEUMXHmhAqmE6JaUgEoUp3Zer3nfln/5L2ac2xa87tWaV+VRRRRvvoAB0jB52jOrpBTdRCFOXoCb2iN+PBeDSejZdva8kobnbRLxjvX+MUkIk=</latexit><latexit sha1_base64="1VwU09zYrtkQ/ZOTO0Qy+yGIBCA=">AAAB+HicbVDLSsNAFJ3UV42vqLhyM1i0rmoigm6EohRcVrAPaEKZTG+aoZMHMxOhhv6LrkTd+R3+gH/jtGah1bM6955z4dzjp5xJZdufRmlhcWl5pbxqrq1vbG5Z2zttmWSCQosmPBFdn0jgLIaWYopDNxVAIp9Dxx9dT/XOPQjJkvhOjVPwIjKMWcAoUXrVt/Ya1aPL0I2zKnZdM9VDo3pC+1bFrtkz4L/EKUgFFWj2rQ93kNAsglhRTqTsOXaqvJwIxSiHielmElJCR2QIPU1jEoH08ln8CT4MEoFVCHg2//TmJJJyHPnaExEVynltuvxP62UquPByFqeZgphqi9aCjGOV4GkLeMAEUMXHmhAqmE6JaUgEoUp3Zer3nfln/5L2ac2xa87tWaV+VRRRRvvoAB0jB52jOrpBTdRCFOXoCb2iN+PBeDSejZdva8kobnbRLxjvX+MUkIk=</latexit>

Conclusiones

• El electrón es una partícula con carga y masa medibles

• El espectro de la radiación térmica se explica apropiadamente usando la hipótesis (Planck) de que la radiación se absorbe y emite en términos enteros de una unidad mínima de energía

• El efecto fotoeléctrico se explica correctamente si se permite que la radiación incidente tenga una energía que sólo dependa de la frecuencia

• La dispersión de Compton se explica adecuadamente si suponemos que la luz se comporta como una partícula con energía ℎ" y momento # = %/'

Entonces… ¿la luz es una partícula?

propiedades de particula · •1879: ley de stefan-boltzmann, •1893: ley de desplazamiento de...

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