Chapter 3 – Quantization of Charge, Light, and Energy
3-17. Equation 3-4: R1   T14
3-18. (a) Equation 3-17: E 
(b) E 
R2   T24    2T1   16 T14  16R1
4
hc / 10hc / kT 
hc / 
0.1kT

 0.1
 0.951kT
hc /  kT
hc / kT  / 10 hc / kT 

e
1 e
1 e 1
hc /  0.1hc / kT  10kT
hc / 

 10
 4.59 104 kT
hc /  kT
hc / kT  /  0.1hc / kT 

e
1 e
1 e 1
Equipartition theorem predicts E  kT . The long wavelength value is very close to
kT, but the short wavelength value is much smaller than the classical prediction.
3-19. (a) mT  2.898 103 m  K  T1 
R1   T14
2.898 103 m  K
 107 K
27.0 106 m
and R2   T24  2R1  2 T14
 T24  2T14 or T2  21/ 4 T1   21/ 4  107 K   128K
2.898 103 m  K
(b) m 
 23 106 m
128K
3-20. (a) mT  2.898 103 m  K
(Equation 3-5)
2.898 103 m  K
m 
 1.45 107 m  145nm
4
2 10 K
(b) m is in the ultraviolet region of the electromagnetic spectrum.
58
Chapter 3 – Quantization of Charge, Light, and Energy
3-21. Equation 3-4: R   T 4
Pabs  1.36 103W / m2  RE2 m2  where RE = radius of Earth
Pemit   RW / m2  4 RE2   1.36 103W / m2  RE2 m2 
  RE2
R  1.36 103W / m2  
2
 4 RE
T4 
 1.36 103 W
 T 4

2
4
m

1.36 103W / m2
 T  278.3K  5.3C
4  5.67 108W / m2  K 4 
3-22. (a) mT  2.898 103 m  K  m 
f m  c / m 
2.898 103 m  K
 8.78 107 m  878nm
3300K
3.00 108 m / s
 3.42 1014 Hz
7
8.78 10 m
(b) Each photon has average energy E  hf and NE  40J / s.
N
40 J / s
40 J / s

 1.77 1020 photons / s
34
14
hf m
 6.63 10 J  s 3.42 10 Hz 
(c) At 5m from the lamp N photons are distributed uniformly over an area
A  4 r 2  100 m2 . The density of photons on that sphere is  N / A / s  m2 .
The area of the pupil of the eye is   2.5 103 m  , so the number of photons
2
entering the eye per second is:
n   N / A   2.5 10 m 
3
2
1.77 10

20
/ s     2.5 103 m 
100 m2
 1.77 1020 / s     2.5 103 m   1.10 1013 photons / s
2
59
2