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प्रश्न
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.
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उत्तर
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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Given the following data for incident wavelength and the stopping potential obtained from an experiment on the photoelectric effect, estimate the value of Planck's constant and the work function of the cathode material. What is the threshold frequency and corresponding wavelength? What is the most likely metal used for emitter?
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