When a metallic surface is illuminated with radiation of wavelength \lambda, the stopping potential is V. If the same surface is illuminated with radiation of wavelength 2\lambda, the stopping potential is\frac{\text{V}} {\text{4}}. The threshold wavelength for the metallic surface is:

  • Option 1)

    4\lambda

  • Option 2)

    5\lambda

  • Option 3)

    \frac{\text{5}} {2}\lambda

  • Option 4)

    3\lambda

 

Answers (1)

 

Conservation of energy -

h\nu = \phi _{0}+\frac{1}{2}mv^{2}_{max}

h\nu = h\nu _{0}+\frac{1}{2}mv^{2}_{max}

 

h\left ( \nu-\nu _{0} \right )=\frac{1}{2}mv^{2}_{max}

where, h - Plank's constant\ \nu - Frequency\ \nu_{0} - threshold\ frequency\ \phi_{0}- work function

- wherein

 

Let threshold wavelength is {\lambda_{0} }

Then  ev=\frac{hc}{\lambda }-\frac{hc}{\lambda_{0} } ---------------(1)

\frac{ev}{4}=\frac{hc}{2\lambda }-\frac{hc}{\lambda_{0} } -------------------(2)\times 4

\Rightarrow ev=\frac{2hc}{\lambda }-\frac{4hc}{\lambda_{0} } ---------------(3)

From equation (1) and (2)

\frac{2hc}{\lambda }-\frac{4hc}{\lambda_{0} }=\frac{hc}{\lambda }-\frac{hc}{\lambda_{0} }

or

\frac{hc}{\lambda_{0} }=\frac{3hc}{\lambda_{0} } \: or \: \lambda _{0}=3\lambda


Option 1)

4\lambda

This is incorrect option

Option 2)

5\lambda

This is incorrect option

Option 3)

\frac{\text{5}} {2}\lambda

This is incorrect option

Option 4)

3\lambda

This is correct option

Most Viewed Questions

Preparation Products

Knockout NEET 2024

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 40000/-
Buy Now
Knockout NEET 2025

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 45000/-
Buy Now
Knockout NEET 2021 (One Month)

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 14000/- ₹ 4999/-
Buy Now
Knockout NEET 2021

Personalized AI Tutor and Adaptive Time Table, Self Study Material, Weekend Live Classes, Unlimited Mock Tests and Personalized Analysis Reports, 24x7 Doubt Chat Support,.

₹ 22999/- ₹ 9999/-
Buy Now
Test Series NEET 2021

Chapter/Subject/Full Mock Tests for NEET, Personalized Performance Report, Weakness Sheet, Complete Answer Key,.

₹ 6999/- ₹ 2999/-
Buy Now
Boost your Preparation for NEET 2021 with Personlized Coaching
 
Exams
Articles
Questions