A Cs plate is irradiated with a light of wavelength `lamda=(hc)/(phi)`,`phi` being the work function of the plate, h Plank's constant, and c the velocity of light in vacuum. Assume all the photoelectron are moving perpendicular to the plate toward a YDSE setup when accelerated through a potential difference V. Take charge on a proton `=e` and moss of an electron `=m`. Read the paragraph carefully and answer the following question:The fringe width due to the electron beam is

Options

A. `(lamdaD)/(d)`
B. `(lamdaD)/(2d)`
C. `(hD)/((dsqrt(2emV)))`
D. none of these

Answer

C

Explanation

`(1)/(2)mv^2=ev`
`v=sqrt((2ev)/(n))`
`lamda=(h)/(mv)=(h)/(sqrt(2mev))`
Fringe width `B=(lamdaD)/(d)`
`=(hD)/(dsqrt(2mev))`