Question

Find the (a) maximum frequency, and (b) minimum wavelength of X-rays produced by 30 kV electrons.

Answer 1

Given: The potential of electrons is 30 kV.

a)

The total energy possessed by the electron is given by,

E=eV

Where, the energy possessed by the electron is E, the charge on the electron is e and the total potential of electrons is V.

By substituting the given values in above equation, we get

E=1.6× 10 −19 ×30× 10 3 =4.8× 10 −15  J

The maximum frequency of X-rays is given as,

E=hν

Where, the Plank’s constant is h and the maximum frequency is ν.

By substitute the given values in above equation, we get

4.8× 10 −15 =6.626× 10 −34 ×ν ν= 4.8× 10 −15 6.626× 10 −34 =7.24× 10 18  Hz

Thus, the maximum frequency of the X-rays produced is 7.24× 10 18  Hz.

b)

The minimum wavelength of X-rays is given as,

λ= c ν

Where, the speed of light is c.

By substituting the given values in above equation, we get

λ= 3× 10 8 7.24× 10 18 =4.14× 10 −11  m =0.0414 nm

Thus, the minimum wavelength of the X-rays is 0.0414 nm.