Photon of energy 2.0 eV and wavelength `lamda`fall on a metal plate and release photoelectrons with a maximum velocity v. By decreasing `lamda`by25% the maximum velocity of photoelectrons is doubled .The work function of the material of the metal plate in eV is

Options

A. 2.22
B. 1.985
C. 2.35
D. 1.8

Answer

D

Explanation

The Einstin Photoelectric equation is given as ,
`(K.E)_(amx)=(1)/(2)mv^(2)=(hc)/(lamda)-w`Case1:`(K.E)_(amx)=(1)/(2)mv^(2)=(hc)/(lamda)-w` (1)
CaseII:`(1)/(2)m(2v)^(2)=(hc)/(lamda-lamdaxx(25)/(100))-w=(4hc)/(3lamda)-w`
`implies4((1)/(2)mv^(2))=(4)/(3)(hc)/(lamda)-w`
`4((hc)/(lamda)-w)=(4)/(3)(hc)/(lamda)-w`(`because`From equation (1))
`implies4(hc)/(lamda)-4w=(4)/(3)(hc)/(lamda)-w`
`-4w+w=(4)/(3)=(hc)/(lamda)-4(hc)/(lamda)`
`3w=4(hc)/(lamda)-(4)/(3)(hc)/(lamda)=(hc)/(lamda)(4-(4)/(3))`
`=(hc)/(lamda)((12-4)/3)=(hc)/(lamda)(8)/(3)``w=(8)/(9.)(hc)/(lamda.)=(8)/(9).2=(16)/(9)=1.8eV`