For the same objective, the ratio of least separation between two points to be distiguised by a microscope for light of `5000 Å` and electrons acclerated through 100V used as illuminating substance is __________ (neraly)

Options

A. `2xx10^(-4)`
B. `2xx10^(-3)`
C. `2xx10^(-2)`
D. `4xx10^(-4)`

Answer

A

Explanation

`d_(min)=(1.22lamda)/(2sinbeta)`
where `beta` is the angle subtended by te objective at the object ltBrgt for light of 5500 Å
`d_(min)=(1.22xx5.5xx10^(-7))/(2sinbeta)m` ltbr. For electrons accelerated through 100 V the deBroglie wavelength is
`lamda=(h)/(p)=(1.227)/(sqrt(100))=0.13xx10^(-9)m`
`therefored'_(min)=(1.22xx1.3xx10^(-10))/(2sinbeta)`
`therefored'_(min)=(1.22xx1.3xx10^(-10))/(2sinbeta)`
`(d'_(min))/(d_(min))=(1.3xx10^(-10))/(5.5xx10^(-7))~0.2xx10^(-3)`