When photon of wavelength `lambda_(1)` are incident on an isolated shere supended by an insulated , the corresponding stopping potential is found to be `V`. When photon of wavelength `lambda_(2)` are used , the orresponding stopping potential was thrice the above value. If light of wavelength `lambda_(3)` is used , carculate the stopping potential for this case.

Options

A. `(hc)/e(1/lamda_3-1/lamda_2-1/lamda_1)`
B. `(hc)/e(1/lamda_3+1/lamda_2-1/lamda_1)`
C. `(hc)/e(1/lamda_3+1/(2lamda_2)-3/(2lamda_1))`
D. `(hc)/e(1/lamda_3+1/(2lamda_2)-1/(lamda_1))`

Answer

C

Explanation

`(hc)/lamda_1=phi+eV" "...(i)`
`(hc)/lamda_2=phi+e(3V)" "...(ii)`
`(hc)/lamda_3=phi+eV. " "...(iii)`
From equation (i) and (ii)
`(hc)/lamda_2=phi+3((hc)/lamda_1-phi)`
`(hc)/lamda_2=(3hc)/lamda_1-2phi`
`2phi=((-hc)/lamda_2+(3hc)/lamda_1)`
From equation (iii)
`(2hc)/lamda_3=2phi+2eV.`
`(2hc)/3=((-hc)/lamda_2+(3hc)/(lamda_1))+2eV.`
`V.=1/(2e)[(2hc)/lamda_3+(hc)/lamda_2-(3hc)/lamda_1]`
`V.=(hc)/e[1/lamda_3+1/(2lamda_2)-3/(2lamda_1)]`
This is required stopping potential.