Quantrex Quantrex AcademyJEE · NEET · NDA PYQs with solutions Open app
NEETPhysicsDual Nature of Matter

Light of wavelength is incident on a photosensitive surface with a work function W > 0 . The fastest emitted photoelectron has a de-Broglie wavelength ₁ . When the incident wavelength is changed to 2 , the fastest photoelectron has a de-Broglie wavelength ₂ . Which of the following inequalities correctly relates ₁ and ₂ ?

Options

  1. A₂ < ₁ 2
  2. B₂ = ₁ 2
  3. C₂ > ₁ 2
  4. D₂ < ₁ 2

Correct answer

A. ₂ < ₁ 2

Step-by-step solution

From Einstein's photoelectric equation, the maximum kinetic energy for the initial wavelength is: K₁ = hc - W When the incident wavelength is halved to 2 , the new maximum kinetic energy is: K₂ = hc /2 - W = 2hc - W We can express K₂ in terms of K₁ : K₂ = 2 (K₁ + W ) - W = 2K₁ + W Since the work function W > 0 , it follows that K₂ > 2K₁ . The de-Broglie wavelength is inversely proportional to the square root of the kinetic energy ( _d = h 2mK ). Therefore, for the new wavelength: ₂ = h 2mK₂ Since K₂ > 2K₁ , we have

Practice Dual Nature of Matter on Quantrex Academy →

More from Dual Nature of Matter

An electron and positron are accelerated from rest to the same kinetic energy. The ratio of their de Broglie wavelengths is 2026An electron of mass m and charge e initially at rest gets accelerated by a constant electric field E. The de-Broglie wavelength of the electron at time t is (h = Planck's constant) 2026The wavelength _e of an electron and _P of a photon of same energy E are related as 2026A light of wavelength ( < ₀) falls on a metal surface. The momentum of the fastest moving electron is p . In order to have the momentum of an electron equal to 2p , the required wa 2026The de Broglie wavelength of an electron with kinetic energy K₁ is ₁ . If the kinetic energy increases to 5K₁ , the new wavelength is ₂ = x ₁ . The value of x is 2026A student plots two different graphs using the same photoelectric experiment data. 1. Maximum kinetic energy ( K_ max ) against frequency ( ) 2. Stopping potential ( V_o ) against 2026In a photoelectric cell, for the incident radiation of wavelength , the fastest electron has speed 'v'. If the wavelength of incident radiation is changed to 3 , the speed of the f 2026A particle is dropped from a height ' y '. The de-Broglie wavelength of the particle as a function of height is 2026 Full Dual Nature of Matter list All NEET PYQs