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प्रश्न
The threshold wavelength of tungsten is 2.76 x 10-5 cm.
(a) Explain why no photoelectrons are emitted when the wavelength is more than 2.76 x 10-5 cm.
(b) What will be the maximum kinetic energy of electrons ejected in each of the following cases
(i) if ultraviolet radiation of wavelength λ = 1.80 × 10-5 cm and
(ii) radiation of frequency 4 x 1015 Hz is made incident on the tungsten surface?
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उत्तर
Data: λ0 = 2.76 x 10-5 cm = 2.76 x 10-7 m,
λ = 1.80 × 10-5 cm = 1.80 × 10-7 m,
v = 4 × 1015 Hz,
h = 6.63 × 10-34 J.s,
c = 3 × 108 m/s
(a) For λ > λ0,v < v0 (threshold frequency).
∴ hv < hv0. Hence, no photoelectrons are emitted.
(b) Maximum kinetic energy of electrons ejected
`= "hc" (1/lambda - 1/lambda_0)`
`= (6.63 xx 10^-34)(3 xx 10^8)(10^7/1.8 - 10^7/2.76)`J
= (6.63 × 10-19)(3)(0.5555 - 0.3623)
= (6.63)(3)(0.1932 × 10-19)J
= 3.842 × 10-19J
`= (3.842 xx 10^-19 "J")/(1.6 xx 10^-19 "J"//"eV")`
= 2.40 eV
(c) Maximum kinetic energy of electrons ejected
= hv - `"hc"/lambda_0`
`= (6.63 xx 10^-34)(4 xx 10^15) - ((6.63 xx 10^-34)(3 xx 10^8))/(2.76 xx 10^-7)`
= 26.52 × 10-19 - 7.207 × 10-19
= 19.313 × 10-19 J
= `(19.313 xx 10^19 "J")/(1.6 xx 10^-19 "J"//"eV")`
= 12.07 eV
संबंधित प्रश्न
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?
| Incident wavelength (in Å) | 2536 | 3650 |
| Stopping potential (in V) |
1.95 | 0.5 |
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