For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of 5000 and electrons accelerated through 100V used as the illuminating substance.

Question

For the same objective, find the ratio of the least separation between two points to be distinguished by a microscope for light of 5000 and electrons accelerated through 100V used as the illuminating substance.

Philoid · Accepted Answer

Least separation is given by … (i) , where λ = wavelength, β = angle subtended by the objective at the object.

For light of wavelength 5000 , .. (ii)

For electron accelerated through 100 V, the De- Broglie wavelength is given by , where h = Planck’s constant = 6.63 x 10^-34 kgm²s^-1, p = momentum.

Now, kinetic energy of electron is given by , where e = electronic charge, V = voltage through which electrons are accelerated, p = momentum, m = mass of electron. Therefore,

.

Hence,

Hence, least separation in this case is given by … (iii)

Hence, required ratio (Ans)