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.

Question

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]

Smart Achievers · Accepted Answer

(7)

From $\frac{h c}{λ} - ϕ = - e V_{0}$

Stopping potential $V_{0} = \frac{1}{e} [\frac{h c}{λ} - ϕ]$

where $h c = 1240 eV - nm$

$= \frac{1}{e} [\frac{1240}{200} - 4.7] = \frac{1}{e} [6.2 - 4.7] = \frac{1}{e} \times 1.5 eV = 1.5 V$

But $V = \frac{1}{4 π ε_{0}} \frac{q}{r} = \frac{1}{4 π ε_{0}} \frac{n e}{r}$ $(n = no. of photo-electrons emitted)$

$\Rightarrow n = \frac{V r (4 π ε_{0})}{e} = \frac{1.5 \times 10^{- 2}}{9 \times 10^{9} \times 1.6 \times 10^{- 19}}$

$∴$ $n = 1.04 \times 10^{7}$

Comparing it with $A \times 10^{z}$ , we get, $z = 7$

Solution

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Solution

Ans. (7) From hcλ-ϕ=-eV0 Stopping potential V0=1e[hcλ-ϕ] where hc=1240 eV-nm =1e[1240200-4.7]=1e[6.2-4.7]=1e×1.5 eV=1.5 V But V=14πε0qr=14πε0ner (n=no. of photo-electrons emitted) ⇒n=Vr(4πε0)e=1.5×10-29×109×1.6×10-19 ∴ n=1.04×107 Comparing it with A×10z, we get, z=7

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