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

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): For a given energy E (where E is much less than the rest mass energy), the de Broglie wavelength of an electron is significantly greater than the wavelength of a photon of the same energy. Reason (R): For the same energy E , the momentum of a non-relativistic electron is greater than the momentum o

Options

  1. ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
  2. BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
  3. CAssertion (A) is true but Reason (R) is false
  4. DAssertion (A) is false but Reason (R) is true

Correct answer

D. Assertion (A) is false but Reason (R) is true

Step-by-step solution

For a photon of energy E , its momentum is p_p = E c . For a non-relativistic electron of kinetic energy E , its momentum is p_e = 2mE . The ratio of their momenta is p_e p_p = 2mE E/c = 2mc^2 E . Since the electron is non-relativistic, its kinetic energy E is much less than its rest mass energy mc^2 ( E mc^2 ). Thus, p_e p_p 1 , which means p_e > p_p . The Reason (R) is true. According to the de Broglie relation, wavelength is inversely proportional to momentum ( = h p ). Since the electron has a greater momentum

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