Physical Chemistry , 1st ed.

Example 9.5

a.What is the energy of one quantum of light that has a wavelength of

11,592 Å? You will need to use the relationship cto convert the wave-

length to a frequency. Use c3.00 

108 m/s.

b.What is the energy of one quantum of light whose frequency is given as

20,552 cm^1?

Solution

a. 3.00 

108 m/s 11,592 Å

1

1

01

m

 (^0) Å
2.59
1014 s^1
Now, using Planck’s formula from equation 9.21:
E6.626
10 ^34 Js 2.59
1014 s^1
E1.71
10 ^19 J
This is not a lot of energy. Understand, however, that this is only the energy
of a single quantum of light.
b.The frequency 20,552 cm^1 must be converted to units of s^1 in order to
use Planck’s constant directly. With these units,
wavenumber 
(^1) 
so one can rearrange to get

waven

1

umber





20.552

1

cm^1



4.8728 

10 ^5 cm 4.8728 

10 ^7 m

Using cor c/ :



4

3

.8

.0

7

0

28

10

1

8

0 

m

7

/

m

s



6.16 

1014 s^1

Using Planck’s constant in conjunction with this frequency:

E(6.626 

10 ^34 Js)(6.16 

1014 s^1 )

E4.08 

10 ^19 J

This again is not a lot of energy.

Example 9.6

Work functions,, are usually listed in units of electron volts, eV, where

1 eV 1.602 

10 ^19 J. What is the velocity of an electron emitted by Li

( 2.90 eV) if light having a frequency of 4.77 

1015 s^1 is absorbed?

260 CHAPTER 9 Pre-Quantum Mechanics