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Chemistry 482 Spring 2013Problem Set 1

Due Friday, Feb. 1, 2013

Problem 1: At what wavelength does the maximum in the energy-density distribution function for a blackbody occurat a Temperature of 600 K? What is the color of a blackbody at this temperature?

Problem 2: In a photoelectric effect experiment, a gold surface is irradiated with laser light with a wavelength of

186 nm .

a. How much energy (in Joules) is contained in each photon of laser light?

b. Given gold's work function of 4.3 eV, what will be the maximum velocity (in m/s) of the

photoelectrons emitted?

c. If the laser power is 30 mW, what is the maximum number of photoelectrons that can be

released per second?

Problem 3: In an electron microscope a beam of electrons is accelerated to a kinetic energy of 200,000 Volts and

focused onto the sample specimen. What is the de Broglie wavelength for the electrons in this beam?

Problem 4: If z = 2x + 3iy provide

(a) Re(z*) (b) Re(z2) (c) Im (z

2) (d) Re(z*z) Im(z*z)

Problem 5: Express the following numbers in the polar formi

z re

(a)14 (b)14i (c)9+3i (d) 9-2i

Problem 6: Express the following numbers in the form z = x + yi

(a)18

18i

e (b) 2 2i ie e (c) 2 2i ie e

Problem 7: Use Euler's formula, cos sinie i , to show that

(cos sin ) (cos sin )n n n nz r i r n i n

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\-r +

-:,.

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\>~ '-

Cf:4..1 'A =- \ "'6'~ "--" -=-")

IL

2.

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i = ,.2 'X -t 3iif .(0) R(,)~")::: R.e(J?(-3i~)=[3X ~ 2l

(bl Re.. U(l::: Re ( 2'X + 3i(j) ( .2')( + 37'(j.J-,

- Re ( 4rxZ T bi':x~ + 61;'51'1 - cr ~.l )

- G-?