Modern Physics 2 Question 28
27. A silver sphere 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 photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $A \times 10^{Z}$ (where $1<A<10$ ). The value of $Z$ is
(2011)
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Solution:
- Photo emission will stop when potential on silver sphere becomes equal to the stopping potential.
$$ \begin{aligned} & \therefore \quad \frac{h c}{\lambda}-W=e V _0 \\ & \text { Here, } \quad V _0=\frac{1}{4 \pi \varepsilon _0} \frac{z e}{r} \\ & \therefore \quad \frac{1240}{200} eV-(4.7 eV)=\frac{9 \times 10^{9} \times n \times 1.6 \times 10^{-19}}{10^{-2}} \\ & (6.2-4.7)=\frac{9 \times 10^{9} \times n \times 1.6 \times 10^{-19}}{10^{-2}} \\ & \text { or } \quad z=\frac{1.5 \times 10^{-2}}{9 \times 1.6 \times 10^{-10}} \\ & =1.04 \times 10^{7} \end{aligned} $$
$\therefore$ Answer is 7 .
