When radiations of wavelength `lamda_(1) and lamda_(2)` are incident on certain photosensitive material, the energies of electron ejected ar `E_(1) and E_(2)` respectively, such that `E_(1)gt E_(2),` Then Planck's constant 'h' is (C = velocity of light)

Options

A. `((E_(1)-E_(2))(lambda_(1)-lambda_(2)))/(c(lambda_(1)*lambda_(2)))`
B. `((E_(1)-E_(2))lambda_(1)c)/((lambda_(1)-lambda_(2))lambda_(2))`
C. `((E_(1)-E_(2))lambda_(1)lambda_(2))/(c(lambda_(2)-lambda_(1)))`
D. `((lambda_(2)-lambda_(1))c)/((E_(1)-E_(2))lambda_(1)*lambda_(2))`

Answer

C

Explanation

`hv=phi+1/2 mv^(2) " " :'v=c/lambda "and" 1/2 mv^(2)=E`
`:.(hc)/(lambda_(1))=phi+E_(1)` ...(1)
and `(hc)/(lambda_(2))=phi+E_(2)` ...(2)
`:'E_(1) gt E_(2)`
`:.` from (1) and (2)
`:.(hc)/(lambda_(1))-(hc)/(lambda_(2))=E_(1)-E_(2)`
`:.hc[(1)/(lambda_(1))-(1)/(lambda)]=E_(1)-E_(2)`
`:.hc[(lambda_(2)-lambda_(1))/(lambda_(1)lambda_(2))]=E_(1)-E_(2)`
`:.h=((E_(1)-E_(2))lambda_(1)lambda_(2))/(c(lambda_(2)-lambda_(1)))` ... option (c)