Practice questions

Chapter 16Atoms, Spectra and Quanta

maxT = const where const = 2.898 × 10-3 m Kσ = 5.67 x 10-8 W m-2 K-4

e = 1.602×10-19 Ch = 6.626×10-34 J s = 4.136×10-15 eV s me = 9.11×10-31 kg

1. An electrically heated radiator is kept at a temperature of 40°C. It has a surface area of 2 m2 and is rated at 2 kW.

a What is the wavelength at which it radiates maximum power?

...................................................................................................................................

.............................................................................................................................. [2]

b i How much energy does it radiate per second? You should find that it radiates at a rate significantly less than 2 kW.

...................................................................................................................................

.............................................................................................................................. [2]

ii Suggest what happens to the remainder of the energy transferred to the radiator each second.

...................................................................................................................................

.............................................................................................................................. [2]

[Total: 6]

2. The eye is most sensitive to light with a wavelength of 560 nm. At what temperature would a (black) body radiate most strongly at this temperature'?

...................................................................................................................................

.............................................................................................................................. [2]

[Total: 2]

1(4)

3. a Explain what is meant by photoelectric emission, and describe the condtions needed to make it occur.

...................................................................................................................................

...................................................................................................................................

...................................................................................................................................

.............................................................................................................................. [4]

b A photoelectric cell is to be used as a light detector as set up as in the circuit in Fig 16.a

[Fig 16.a]

i For a fixed wavelength of the light incident on the cathode of the photoelectric cell, the reading on the ammeter is proportional to the intensity. Explain why this is so.

...................................................................................................................................

.............................................................................................................................. [2]

ii Light of wavelength 656 nm and power 0.75 W is incident on the cathode of the photoelectric cell. If 40% of the incident photons result in electrons contributing towards current in the circuit, calculate the reading on the ammeter.

...................................................................................................................................

...................................................................................................................................

.............................................................................................................................. [4]

c The equation for the photoelectric effect is EK, max = hf – W

The threshold (maximum) wavelength that produces photo-emission in this photoelectric cell is 1·78 ×10–6 m. Calculate the work function in eV of the metal from which the cathode is made.

...................................................................................................................................

...................................................................................................................................

.............................................................................................................................. [3]

[Total: 13]

2(4)

4. The work functions of three metals are shown in the table:

eV J/10-19

potassium 1.81 2.9sodium 2.28 3.65zinc 4.31 6.9

a Which metal will show the photoelectric effect with the lowest frequency of radiation?

...................................................................................................................................

.............................................................................................................................. [2]

b Calculate the minimum (threshold) frequency that can cause the emission of electrons from zinc.

...................................................................................................................................

.............................................................................................................................. [2]

c What other propertyies of sodium suggest that it is fairly easy for its atoms to lose electrons?

...................................................................................................................................

.............................................................................................................................. [2]

d Monochromatic light of wavelength 500 nm shines on a clean potassium surface. What is the maximum kinetic energy of the electrons emitted?

...................................................................................................................................

.............................................................................................................................. [2]

[Total: 8]

5. Elements may be identified by their line spectra.

a Describe briefly an experiment to observe the line spectrum of an element and measure the wavelengths of its lines.

...................................................................................................................................

.............................................................................................................................. [3]

b Briefly explain the physical reasons why the line spectra of different elements are unlikely to be identical.

...................................................................................................................................

.............................................................................................................................. [3]

[Total: 6]

3(4)

6. This question compares the diffraction of light (see Chapter 15) with the diffraction of electrons.

a A diffraction grating is set up to form a spectrum of white light. Which of the blue or red light is diffracted through the larger angle?

(n =d sin)

...................................................................................................................................

.............................................................................................................................. [2]

b A diffraction grating has a grating spacing d of 5 x 10-6 m. By what angle is the first order maximum produced for light of wavelength 5.0 x 10-7 m?

...................................................................................................................................

.............................................................................................................................. [2]

c A student considers using the grating to produce the diffraction of electrons. He intends to place the grating in a vacuum tube and fire a beam of electrons at it. The emerging electron beam would be displayed using a fluorescent screen as used in cathode ray tubes. The arrangement would be good enough to detect a diffraction angle of 2°.

(1 eV =1.6 x 10-19 J, for electrons momentum p =h, kinetic energy EK = p2/2m.)

i The detecting screen only works if the electrons hitting it have been accelerated by a potential difference of 2 kV. What is the wavelength of electrons that have been accelerated by this voltage?

...................................................................................................................................

.............................................................................................................................. [3]

ii If the grating is capable of diffracting electrons, what would be the angle of the first order maximum for these electrons'? Is the experiment feasible?

...................................................................................................................................

.............................................................................................................................. [2]

[Total: 9]

7. A neutron has a mass of 1.67 x 10-27 kg. Slow neutrons ('thermal' neutrons) are used in nuclear power stations to initiate the fission of uranium fuel. Such neutrons have an average kinetic energy of 0.04 eV. (1 eV is 1.6 x 10-19 J.)

a Calculate the momentum of neutrons which have this value of kinetic energy.

...................................................................................................................................

.............................................................................................................................. [2]

b Use the de Broglie formula to calculate the wavelength of neutrons with this energy.

...................................................................................................................................

.............................................................................................................................. [2]

[Total: 4]

[Total for test paper: 48]

4(4)