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
- ABoth Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A)
- BBoth Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A)
- CAssertion (A) is true but Reason (R) is false
- 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