A silver sphere of radius 1cm and work function $4.7 e V$ is suspended from an insulating thread in free-space. It is under continuous illumination of $200 n m$ 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 _________

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answer is 7.

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Detailed Solution

Photo emission will stop when potential on silver sphere becomes equal to the stopping potential.
$∴ \frac{h c}{λ} - W = e V_{0}$
Here, $V_{0} = \frac{1}{4 π \in_{0}} \frac{z e}{r}$ $∴ \frac{h c}{λ} - W = \frac{1}{4 π \in_{0}} \frac{n e^{2}}{r}$ $∴ (\frac{1240}{200} e V) - (4.7 e V)$

$= \frac{9 \times 10^{9} \times n \times 1.6 \times 10^{- 19}}{10^{- 2}}$ $(6.2 - 4.7) \times 1.6 \times 10^{- 19}$ $= \frac{9 \times 10^{9} \times n \times {(1.6 \times 10^{- 19})}^{2}}{10^{- 2}}$ $o r n = \frac{1.5 \times 10^{- 2}}{9 \times 1.6 \times 10^{- 10}} = 1.04 \times 10^{7} = 7$