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

Answer

a

Explanation

`1/2mu_(1)^(2)=(hc)/(lambda_(1))-phi_(0) , 1/2mu_(2)^(2)=(hc)/(lambda_(2))-phi_(0)`
`(u_(1)^(2))/(u_(2)^(2)) =((hc)/(lambda_(1))-phi_(0))/((hc)/(lambda_(2))-phi_(0))` or `(2/1)^(2)=((hc)/(lambda_(1))-phi_(0))/((hc)/(lambda_(2))-phi_(0))`
or `(4hc)/(lambda_(2))-4phi_(0)=(hc)/(lambda_(1))-phi_(8)`
`(4hc)/(lambda_(2))-(hc)/(lambda_(1))=3phi_(0)`
or `phi_(0)=1/3[(4hc)/(lambda_(2))-(hc)/(lambda_(1))]=1/3[4xx1240/310-1240/248]`
`=1/3[16-5]~~3.7 eV`