22. What is the frequency of light emitted when the electron in a hydrogen atom

Question

22.   What is the frequency of light emitted when the electron in a hydrogen atom undergoes a transition from level n = 7 to level n = 3? (c = 3.00 ´ 108 m/s, h = 6.63 ´ 10-34 J × s), RH = 2.179 × 10-18 J)
A)   2.98 × 1014 Hz
B)   1.98 × 10–19 Hz
C)   1.52 × 1027 Hz
D)   9.94 × 105 Hz
E)   1.01 × 10–6 Hz

23.   What is the wavelength of an electron traveling at 8.50% of the speed of light? (me = 9.109 ´ 10-31 kg, c = 3.00 ´ 108 m/s, h = 6.63 ´ 10-34 J × s)
A)   2.85 × 10–11 m
B)   2.43 × 10–12 m
C)   2.85 × 10–13 m
D)   3.50 × 1010 m
E)   3.50 × 1012 m

Explanation / Answer

22. Answer A

delta E = (-2.179 * 10^-18 J) [1/(3)^2 - 1/(7)^2]
= (-2.179 * 10^-18 J) (0.09)
= - 1.9611 * 10^-19 J

frequency (nu) = delta E / h
= (1.9611 * 10^-19 J) / (6.63 * 10^-34 J*s)
= 2.96 * 10^14 s^-1

23. answer A.

wavelength = h/mc

0.085 *3x10^8 = 0.255x10^8

0.255x10^8 * 9.109x10^-31= 2.323x10^-23

6.63x10^-34 /2.323x10^-23

= 2.85x10^-11

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