n ¼
Q
e
¼
I Â t
e
¼
3 Â 10
À2
 1
1:6 Â 10 À19 ¼ 1:87 Â 10
17
=s
Further, we have
eV ¼
1
2
mv
2 or v
2
¼
2eV
m
¼
2 Â 1:6 Â 10
À19
 4  10
4
9:1 Â 10 À31
¼1:406 Â 10
16
or v ¼ 1:19 Â 10
8 m/s
and k min ¼
hc
eV max
¼
6:626 Â 10
À34
 3  10
8
1:6 Â 10 À19 Â 4 Â 10 4
¼ 3:11 Â 10
À11 m ¼ 0:311 ˚
A
Example 3 Electrons bombarding the anode of a Coolidge tube produce X-rays of
wavelength 1 Å. Determine the energy of each electron at the time of impact.
Solution: Given: k = 1 Å = 10
À10 m, energy of each electron at the time of
impact = ?
Energy of an electron at the time of impact is given by
DE =
hc
ek
¼
6:626 Â 10
À34
 3  10
8
1:6 Â 10 À19 Â 10 À10 ¼ 1:24 Â 10
4 eV
Example 4 Calculate Planck’s constant when an X-ray tube operating at 30 kV
emits a continuous X-ray spectrum which has k min ¼ 0:414 ˚
A :
Solution: Given: Operating voltage of the X-ray tube = 30 kV = 30 Â
10
3
V; k min ¼ 0:414 ˚
A ¼ 0:414 Â 10
À10 m; h = ?
We know that
eV max ¼ hm max ¼
hc
k min
Therefore,
h ¼
eV max  k min
c
¼
1:6 Â 10
À19
 30  10
3
 0:414  10
À10
3 Â 10 8
¼ 6.624 Â 10
À34 J - s
Example 5 An X-ray tube is operating at 40 kV and tube current 25 mA, deduce
the power input of the tube. If this power is maximum achievable in this tube, then
determine the maximum permissible tube current at 50 kV.
7.1 Production of X-Rays
267