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.

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)


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