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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. - Physics

Answer in Brief

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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Solution

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)(0.5555 - 0.3623)

= (6.63)(0.1932 × 10-19)J = 1.281 × 10-19J

`= (1.281 xx 10^-19 "J")/(1.6 xx 10^-19 "J"//"eV")`

= 0.8006 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

Concept: The Photoelectric Effect
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APPEARS IN

Balbharati Physics 12th Standard HSC Maharashtra State Board
Chapter 14 Dual Nature of Radiation and Matter
Exercises | Q 9 | Page 323
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