Question

a) In an electron microscope, a potential difference of 20 kV is applied to accelerate the electrons. Determine the wavelength (in m) of the X-ray photons of equal energy as said electrons. If the wavelength of the X-rays is between 10 and 0.01 nm, what can you deduce about its calculation? b) An electron and a neutron have the same wavelength of de Broglie.

Answer 1

a) The electron is accelerated by a potential of 20 kV

The energy of a single electron will be

E = e*V = 20 keV (kilo electron volts)

The de broglie wavelength is given by

We have

E = p^2/2m

So,

Taking h = 6.626*10^-34 Js

m = 9.1*10^-31 kg

and E = 20*10^3 * 1.6*10^-19 J

The wavelength is close to 0.1 nm.

This means that the electrons can be used for probing atoms similar to x rays.

b) We have

The mass of a neutron is almost 1800 times that of an electron.

So, its energy will be 1/1800 times for the same de Borglie wavelength.