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Question

Silver has a work function of 4.7 eV. When ultraviolet light of wavelength 100 nm is incident upon it, a potential of 7.7 V is required to stop the photoelectrons from reaching the collector plate. How much potential will be required to stop the photoelectrons when light of wavelength 200 nm is incident upon silver?

A
1.5 V
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B
3.85 V
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C
2.35 V
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D
15.4 V
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Solution

The correct option is A 1.5 V
Einstein's equation for photoelectric effect is given by, eV0=EW
In first case: eV0=7.7eV, where V0 is the cut-off potential and

W=4.7eV, work function of silver metal.

So, Energy of photon is E1=E=eV0+W=7.7+4.7=12.4eV

We know that E=hcλ

If E2 is the photon energy in the second case, E2E1=λ1λ2=100nm200nm=0.5

so E2=0.5E1=0.5(12.4)=6.2eV

If V02 is the cut-off potential in the second case, eV01=E2W (as same metal for both case so W is same for both case)

or eV02=6.24.7=1.5eV

or V02=1.5V

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