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?

Explanation

Limit of resolution of a microscope is
`d_("min") = (1.22 lambda)/(2 sin beta)`
where `beta` is the angle subtended by the objective lens at the object
For `lambda_1 = 5000 Å = 5000 xx 10^(-10)m`, we have
`d_("min") = (1.22 xx 5000 xx 10^(-10))/(2 sin beta)`
When electron accelerated through a voltage of 100 V, de Broglie wavelength associated with them is
`lambda_2 = (1.227)/(sqrt(v)) = (1.227)/(sqrt100) = 0.13 nm`
`= 0.13 xx 10^(-9) m`
`:. d._("min") = (1.22 xx 0.13 xx 10^(-9))/(2 sin beta)`
`implies (d._("min"))/(d_("min")) = (0.13 xx 10^(-9))/(5000 xx 10^(-10)) = 2.6 xx 10^(-4)`.