Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength <math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mi>a</mi><mi>n</mi><mi>d</mi><mtext> </mtext><mtext> </mtext><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub><mo>,</mo></mrow></math> respectively are incident on a metallic surface. If <math><mrow><msub><mrow><mi>λ</mi></mrow><mrow><mn>1</mn></mrow></msub><mo>=</mo><mn>3</mn><msub><mrow><mi>λ</mi></mrow><mrow><mn>2</mn></mrow></msub></mrow></math> then:

E Energy with which photons are incident on a metallic surface.λ1=3λ2⇒λ1>λ2E α1λ, E1 < E2We know E1 = ?0+k1hcλ1=?+k1k1 = hcλ1−?0−−−−(i)& E2 = ?0+k2hcλ2=?0+k23hcλ1=?+k2k2 = 3 hcλ1−?0 (i)from (1) & (2)kz=3[k1+?0]−?0=3k1+2?0k2 > 3k1⇒k23>k1

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Physics Class 12th Dual Nature of Radiation and Matter

Let K₁and K₂ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $λ_{1} a n d λ_{2},$ respectively are incident on a metallic surface. If $λ_{1} = 3 λ_{2}$ then:

Option 1 -

Option 2 -

Option 3 -

1.5

Option 4 -

0.5

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Answered by

alok kumar singh | Contributor-Level 10

2 months ago

Correct Option - 2

Detailed Solution:

E Energy with which photons are incident on a metallic surface.

$λ_{1} = 3 λ_{2} \Rightarrow λ_{1} > λ_{2}$

E $α \frac{1}{λ},$ E₁ < E₂

We know E₁ = $?_{0} + k_{1}$

$\frac{h c}{λ_{1}} = ? + k_{1}$

k₁ = $\frac{h c}{λ_{1}} - ?_{0} - - - - (i)$

& E₂ = $?_{0} + k_{2}$

$\frac{h c}{λ_{2}} = ?_{0} + k_{2}$

$\frac{3 h c}{λ_{1}} = ? + k_{2}$

k₂ = $\frac{3 h c}{λ_{1}} - ?_{0}$ (i)

from (1) & (2)

$k_{z} = 3 [k_{1} + ?_{0}] - ?_{0} = 3 k_{1} + 2 ?_{0}$

k₂ > $3 k_{1} \Rightarrow \frac{k_{2}}{3} > k_{1}$

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Let K₁and K₂ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $λ_{1} a n d λ_{2},$ respectively are incident on a metallic surface. If $λ_{1} = 3 λ_{2}$ then:

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Let K1 and K2 be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength λ1and λ2, respectively are incident on a metallic surface. If λ1=3λ2 then:

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Let K₁and K₂ be the maximum kinetic energies of photo-electrons emitted when two monochromatic beams of wavelength $λ_{1} a n d λ_{2},$ respectively are incident on a metallic surface. If $λ_{1} = 3 λ_{2}$ then: