A silver of radius `1 cm` and work function `4.7 eV` is suspended from an insulating thread in free space. 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^(z) (where 1lt A lt 10)` The value of `z` is

Options

A. 6
B. 7
C. 8
D. 9

Answer

B

Explanation

(b) : Here, radish of sphere `R=cm=1xx10^(-2)m`
Work function, W=4.7 eV
Energy of incident radiation `=(hc)/(lamda)=(1240eVnm)/(200nm)=6.2eV`
According to Einstein's photoelectric equation
`(hc)/(lamda)=phi+eV_(s)`
`6.2eV=4.7eV+eV_(s)`
`V_(s)=1.5V`
The sphere willl stop emitting photoelectrons, when the potential on surface becomes equal to 1.5 V.
`:.(1)/(4piepsilon_(0))(Q)/(R)=1.5rArr(1)/(4piepsilon_(0))(Ne)/(R)=1.5` where N=Number of photoelectrons emitted
e=charge of each electron
`N=(1.5xxR)/((1)/(4piepsilon_(0))xxe)=(1.5xx1xx10^(-2))/(9xx10^(9)xx1.6xx10^(19))`
`N=(15)/(16)xx(1)/(9)xx10^(8)=(5)/(48)xx10^(8)`
`N=(50)/(48)xx10^(7)=1.04xx10^(7)" ":.Z=7`