
Light of frequency \[4{\nu _0}\], is incident on the metal of the threshold frequency \[{\nu _0}\]. The maximum kinetic energy of the emitted photoelectrons is
A. \[3\,h{\nu _0}\]
B. \[2\,h{\nu _0}\]
C. \[\dfrac{3}{2}h{\nu _0} \\ \]
D. \[\dfrac{1}{2}h{\nu _0}\]
Answer
164.4k+ views
Hint:The maximum kinetic energy of the ejected electron during photoelectric effect is the residual energy transferred by the incident photon to the electron after overcoming the work function of the metal surface. The work function of the metal is constant. So, greater will be the photon energy, greater will be the kinetic energy of the emitted photoelectrons.
Formula used:
\[K = h\nu - \phi \]
Here K is the kinetic energy of the emitted electron, h is the planck's constant, c is the speed of light, \[\nu \] is the frequency of the photon and \[\phi \]is the work function of the metal.
Complete step by step solution:
The wavelength that must be present in order to overcome the attractive attraction that holds the valence electron to the metal atom's shell is known as the threshold wavelength of the metal. The wavelength should be the highest permitted wavelength for the minimal value of the photon's energy since the photon's energy is inversely related to its wavelength.
When the kinetic energy is zero, then the corresponding energy of the photon is called the work function of the metal. The frequency corresponding to the energy equivalent to the work function is called the threshold frequency and it is given for the metal is \[{\nu _0}\]. The frequency of the incident light is \[4{\nu _0}\]. Using the formula of maximum kinetic energy, we get
\[{K_{\max }} = 4h{\nu _0} - h{\nu _0}\]
\[\therefore {K_{\max }} = 3\,h{\nu _0}\]
Hence, the maximum kinetic energy of the ejected electron is \[3\,h{\nu _0}\].
Therefore, the correct option is A.
Note: The maximum kinetic energy of the photoelectron is proportional to the frequency of the incident photon. If the frequency of the incident photon is equal to the threshold frequency of the metal, then the maximum kinetic energy is zero as all the energy is used to make electrons come out of the metal surface.
Formula used:
\[K = h\nu - \phi \]
Here K is the kinetic energy of the emitted electron, h is the planck's constant, c is the speed of light, \[\nu \] is the frequency of the photon and \[\phi \]is the work function of the metal.
Complete step by step solution:
The wavelength that must be present in order to overcome the attractive attraction that holds the valence electron to the metal atom's shell is known as the threshold wavelength of the metal. The wavelength should be the highest permitted wavelength for the minimal value of the photon's energy since the photon's energy is inversely related to its wavelength.
When the kinetic energy is zero, then the corresponding energy of the photon is called the work function of the metal. The frequency corresponding to the energy equivalent to the work function is called the threshold frequency and it is given for the metal is \[{\nu _0}\]. The frequency of the incident light is \[4{\nu _0}\]. Using the formula of maximum kinetic energy, we get
\[{K_{\max }} = 4h{\nu _0} - h{\nu _0}\]
\[\therefore {K_{\max }} = 3\,h{\nu _0}\]
Hence, the maximum kinetic energy of the ejected electron is \[3\,h{\nu _0}\].
Therefore, the correct option is A.
Note: The maximum kinetic energy of the photoelectron is proportional to the frequency of the incident photon. If the frequency of the incident photon is equal to the threshold frequency of the metal, then the maximum kinetic energy is zero as all the energy is used to make electrons come out of the metal surface.
Recently Updated Pages
Uniform Acceleration - Definition, Equation, Examples, and FAQs

JEE Main 2021 July 25 Shift 1 Question Paper with Answer Key

JEE Main 2021 July 22 Shift 2 Question Paper with Answer Key

JEE Main 2025 Session 2: Exam Date, Admit Card, Syllabus, & More

JEE Atomic Structure and Chemical Bonding important Concepts and Tips

JEE Amino Acids and Peptides Important Concepts and Tips for Exam Preparation

Trending doubts
Degree of Dissociation and Its Formula With Solved Example for JEE

Charging and Discharging of Capacitor

Instantaneous Velocity - Formula based Examples for JEE

Formula for number of images formed by two plane mirrors class 12 physics JEE_Main

In which of the following forms the energy is stored class 12 physics JEE_Main

JEE Main Chemistry Question Paper with Answer Keys and Solutions

Other Pages
Dual Nature of Radiation and Matter Class 12 Notes: CBSE Physics Chapter 11

Three mediums of refractive indices mu 1mu 0 and mu class 12 physics JEE_Main

Total MBBS Seats in India 2025: Government College Seat Matrix

NEET Total Marks 2025: Important Information and Key Updates

Neet Cut Off 2025 for MBBS in Tamilnadu: AIQ & State Quota Analysis

Karnataka NEET Cut off 2025 - Category Wise Cut Off Marks
