A metal is illumimated by light of two different wavelength `248nm` and `310 nm` . The maximum speeds of the photoelectrons corresponding in these wavelength are `u_(1) and u_(2)` respectively . If the ratio `u_(1) : u_(2) = 2 : 1` and `hc = 1240 eVnm `, the work function of the meal is nearly

Options

A. `3.7 eV`
B. `3.2 eV`
C. `2.8 eV`
D. `2.5 eV`

Answer

A

Explanation

`K_("max")=(hc)/lambda - phi`
`1/2 m u_(0)^(2)=1240/248- phi` …(1)
`1/2 m u_(2)^(2)=1240/310 - phi` …(2)
Dividing, the two equations
`(u_(1)/u_(2))^(2)=(5-phi)/(4-phi)` & `u_(1)/u_(2)=2/1` (given)
`4=(5-phi)/(4-phi) implies phi =11/3=3.7 eV`