A silver of radius `1 cm` and work function `4.7 eV` is suspended from an insulating thread in freepace. It is under continuous illumination of `200 nm` wavelength light. As photoelectron are emitted the sphere gas charged and acquired a potential . The maximum number of photoelectron emitted from the sphere is `A xx 10^(e) (where 1lt A lt 10)` The value of `z` is

Options

A. 5
B. 7
C. 8
D. 10

Answer

B

Explanation

Here , radius of sphere R = 1 cm ` = 1xx10^(-2)` m
Work function , `phi_(0) = 4.7 eV`
Energy of incident radiation
`=(hc)/lamda = (1240 eVnm)/(200 nm) " " (Take hc = 1240 eV nm) `
`= 6.2 eV`
According to Einstein.s photoelectric equation
`(hc)/lamda = phi_(0) + eV_s`
`6.2 eV = 4.7 eV + eV_s`
`V_s = 1.5 V`

The sphere will stop emitting photoelectrons , when the potential its surface becomes equal to 1.5 V
`:. 1/ (4epsilon_0) Q/R = 1.5 " or " 1/(4 piepsilon_0) (Ne)/R = 1.5`
where, N = Number of photoelectrons emitted
e = Charge of each electron
`N=(1.5 xxR)/((1)/(4piepsilon_0)xxe)=(1.5xx1xx10^(-2))/(9xx10^(9)xx1.6 xx10^(-19))`
`N = 15 / 16 xx1/9 xx10^(8) = 5/48 xx10^(8)`
`N = 50/48 xx 10^(7) = 1.04 xx10^(7) :. Z = 7 `