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. 2.8 eV
D. 2.5 eV

Answer

A

Explanation

Ratio of maximum possible kinetic energies can be written as follows :
`k_1/k_2=((u_1)/u_2)^2=4`
`k_1=(hc)/lamda-phi=(1240)/248-phi" "impliesk_1=(5-phi)`
`k_2=1240/310-phi" "impliesk_2=(4-phi)`
`k_1/k_2=((5-phi)/(4-phi))=4 " "5-phi=4(4-phi)`
`" "implies5 - phi = 16 - 4 phi`
`" "implies3phi=11impliesphi=11/3=3.7eV`