Two identical metal plates show photoelectric effect by a light of wavelength `lambda_(A)` falls on plate `A` and `lambda_(B)` on plate `B(lambda_(A) = 2 lambda_(B))`. The maximum kinetic energy is

Options

A. `2K_(A) = K_(B)`
B. `K_(A) lt K_(B)//2`
C. `K_(A) = 2K_(B)`
D. `K_(A) gt K_(B)//2`

Answer

B

Explanation

`(hc)/(lambda_(A)) =phi+K_(A)` ...(i)
`(hc)/(lambda_(B)) =phi+K_(B)` …(ii)
Let `lambda_(A) = lambda, lambda_(B) =lambda//2`
`(K_(B))/(K_(A)) =((hc)/(lambda//2)-phi)/((hc)/(lambda)-phi) =((hc)/(lambda)-phi)/((hc)/(lambda)-phi) +((hc)/(lambda))/((hc)/(lambda)-phi)`
`=1 +(gt1) = gt 2`
`K_(B)gt2 K_(A)`
`K_(A)lt(K_(B))/(2)`