For the same objective, what is the ratio of the least separation between two points to be distinguished by a microscope for light of 5000 Ã… and electrons accelerated through 100 V used as an illuminating substance?

Options

A. 3075
B. 3575
C. 4075
D. 5075

Answer

C

Explanation

The limit of resolution of a microscope is
`d=(lambda)/(2"sin"theta)`
where `2 theta` is the angle of cone of light rays entering the objective of the microscope.
Here, `lambda_(1)=5000 Ã…`
For electrons accelerated through 100 V, de Broglie wavelength,
`lambda_(2)=(12.27)/(sqrt(100))Ã…=1.227Ã…`
As (`2sin theta`) is same in the two cases, therefore,
`(d_(1))/(d_(2))=(lambda_(1))/(lambda_(2))=(5000)/(1.227)=4075`