Light of wavelength `lambda_(A)` and `lambda_(B)` falls on two identical metal plates A and B respectively . The maximum kinetic energy of photoelectrons in `K_(A)` and `K_(B)` respectively , then which one of the following relations is true ? `(lambda_(A) = 2lambda_(B))`

Options

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

Answer

A

Explanation

According to Einstein photoelectric equation
`K_(A) = (hc)/(lambda_(A)) - phi implies 2K_(A) = (2hc)/(lambda_(A)) - 2 phi`
or `2 K_(A) + phi = (2hc)/(lambda_(A)) - phi`
Wavelength of metal B is half of metal A
`therefore 2 K_(A) + phi = K_(B)`
`implies K_(A) lt (K_(B))/(2)`