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Question
Photocurrent recorded in the microammeter in an experimental setup of the photoelectric effect vanishes when the retarding potential is more than 0.8 V if the wavelength of incident radiation is 4950 Å. If the source of incident radiation is changed, the stopping potential turns out to be 1.2 V. Find the work function of the cathode material and the wavelength of the second source.
Solution
Data: VO = 0.8 V, λ = 4950 Å = 4.950 x 10-7 m, `"V"_"O"'` = 1.2 V, h = 6.63 × 10-34 J.s, c = 3 × 108 m/s
1. `"V"_"O""e" = "hv" - phi = "hc"/lambda - phi`
∴ The work function of the cathode material,
`phi = "hc"/lambda - "V"_"O""e"`
`= ((6.63 xx 10^-34)(3 xx 10^8))/(4.950 xx 10^-7) - (0.8)(1.6 xx 10^-19)`
= 4.018 × 10-19 - 1.28 × 10-19
= 2.738 × 10-19 J
`= (2.738 xx 10^-19 "J")/(1.6 xx 10^-19 "J"//"eV")`
= 1.711 eV
2. `"V"_"O"'"e" = "hc"/(lambda') - phi`
∴ `"hc"/(lambda') = "V"_"O"'"e" + phi`
∴ The wavelength of the second source,
`lambda' = "hc"/("V"_"O"'"e" + phi)`
`= ((6.63 xx 10^-34)(3 xx 10^8))/((1.2)(1.6 xx 10^-19) + 2.738 xx 10^-19)`
`= (19.89 xx 10^-26)/(4.658 xx 10^-19)`
= 4.270 × 10-7 m
= 4270 Å
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