Page 429 - Schaum's Outline of Theory and Problems of Applied Physics

414 PHYSICAL AND QUANTUM OPTICS [CHAP. 33

X-RAYS
X-rays are high-frequency electromagnetic waves produced when fast electrons impinge on a target. If the
electrons are accelerated through a potential difference of V , each electron has the energy KE = eV . If all this
energy goes into creating an X-ray photon, then

eV = hf
Electron kinetic energy = X-ray photon energy
and the frequency of the X-rays is f = eV/h.

SOLVED PROBLEM 33.10
In a certain television picture tube, electrons are accelerated through a potential difference of 10,000 V.
Find the frequency of the X-rays emitted when these electrons strike the screen.
Since hf = eV , here we have
4
eV (1.6 × 10 −19 C)(10 V) 18
f = = = 2.4 × 10 Hz
h 6.63 × 10 −34 J·s
SOLVED PROBLEM 33.11
An X-ray tube emits X-rays whose wavelength is 2×10 −11 m. What is the operating voltage of the tube?

The frequency of the X-rays is
8
c 3 × 10 m/s
19
f = = = 1.5 × 10 Hz
λ 2 × 10 −11 m
Since hf = eV ,
19
hf (6.63 × 10 −34 J·s)(1.5 × 10 Hz)
4
V = = = 6.2 × 10 V = 62 keV
e 1.6 × 10 −19 C
ELECTRONVOLT
A common energy unit in atomic and quantum physics is the electronvolt (eV), defined as the energy an electron
gains when it moves through a potential difference of 1 V. Since the charge e of an electron is 1.6 × 10 −19 C,

1eV = 1.60 × 10 −19 J
Multiples of the electronvolt are the kiloelectronvolt (keV), megaelectronvolt (MeV), and gigaelectronvolt (GeV),
where
6
9
3
1keV = 10 eV 1 MeV = 10 eV 1 GeV = 10 eV
SOLVED PROBLEM 33.12
7
What is the kinetic energy in electronvolts of an electron whose velocity is 10 m/s?
2
7
2
1
1
KE = mv = ( )(9.1 × 10 −31 kg)(10 m/s) = 4.55 × 10 −17 J
2 2
Since 1 eV = 1.6 × 10 −19 J,
4.55 × 10 −17 J
KE = = 284 eV
1.6 × 10 −19 J/eV