SATHEE: Atomic Structure 1 Question 26

Atomic Structure 1 Question 26

2. If $p$ is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $λ$ , then for $1.5 p$ momentum of the photoelectron, the wavelength of the light should be

(Assume kinetic energy of ejected photoelectron to be very high in comparison to work function)

(2019 Main, 8 April II)

(a) $\frac{4}{9} λ$

(b) $\frac{3}{4} λ$

(d) $\frac{1}{2} λ$

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Answer:

Correct Answer: 2. (a)

Solution:

The expression of kinetic energy of photo electrons,

$KE = \frac{1}{2} m v^{2} = E - E_{0}$

When, $KE » E_{0}$ , the equation becomes,

$\begin{matrix} KE = \frac{1}{2} m v^{2} = E \Rightarrow \frac{1}{2} m v^{2} = \frac{h c}{λ} \Rightarrow \frac{p^{2}}{2 m^{2}} = \frac{h c}{λ} \Rightarrow λ = h c \times 2 m^{2} \times \frac{1}{p^{2}} \Rightarrow λ \propto \frac{1}{p^{2}} E = \frac{h c}{λ} = energy of incident light. E_{0} = threshold energy or work functions, \frac{1}{2} m v^{2} = \frac{1}{2} \times \frac{(m v)^{2}}{m^{2}} = \frac{1}{2} \times \frac{p^{2}}{m^{2}} \end{matrix}$

$∵ p =$ momentum $= m v$

As per the given condition,

$\frac{λ_{2}}{λ_{1}} = {(\frac{p_{1}}{p_{2}})}^{2}$

$\begin{array}{lll} \Rightarrow & \frac{λ_{2}}{λ} = {(\frac{p}{1.5 \times p})}^{2} = {(\frac{2}{3})}^{2} = \frac{4}{9} \Rightarrow & λ_{2} = \frac{4}{9} λ & [\begin{array}{c} ∵ λ_{1} = λ p_{1} = p \end{array}] \end{array}$

Atomic Structure 1 Question 26

2. If $p$ is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $λ$ , then for $1.5 p$ momentum of the photoelectron, the wavelength of the light should be

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Atomic Structure 1 Question 26

2. If p is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength λ, then for 1.5p momentum of the photoelectron, the wavelength of the light should be

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

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2. If $p$ is the momentum of the fastest electron ejected from a metal surface after the irradiation of light having wavelength $λ$ , then for $1.5 p$ momentum of the photoelectron, the wavelength of the light should be