A metal surface is illuminated by light of two different wavelengths 248 nm and 310 nm. The maximum speeds of the photoelectrons corresponding to these wavelengths are `mu_1` and `mu_2` respectively. If the ratio `u_1: u_2 = 2:1 and hc= 1240 eV` , the work function of the metal is nearly.
(a)3.7 eV (b) 3.2 eV
(c ) 2.8eV (d) 2.5eV.

Options

A. 3.7 eV
B. 3.2 eV
C. 3.8 eV
D. 2.5 eV

Answer

A

Explanation

248 nm =1240 / 248 eV =5eV
310 nm =1240 / 310 eV =4eV
`(K.E_1)/(K.E_2) = (4)/(1) = (5eV-W)/(4eV -W)`
`rArr 16 eV-4W =5eV-W rArr 11 =3 W`
`rArr W = (11)/(3) =3.67 eV ~= 3.7 eV`