Physics Dawn of Modern Physics ETEA 2022
PMDC Verified Question 29 of 52
An electron will have maximum kinetic energy when it has:
A
Short wavelength
B
Long wavelength
C
Low frequency
D
Circular motion
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option A: Short wavelength
Concept:

The momentum and kinetic energy of an electron are fundamentally linked to its de Broglie wavelength.

Formula:

$$ \lambda = \frac{h}{p} = \frac{h}{\sqrt{2m(K.E)}} $$

Solution:

  • Rearranging the formula for kinetic energy yields: \( K.E = \frac{h^2}{2m\lambda^2} \).


  • This demonstrates an inverse square relationship between kinetic energy and wavelength.


  • Therefore, to maximize kinetic energy, the electron must have the smallest (shortest) possible wavelength.


Why other options are incorrect:

A long wavelength implies low momentum and minimal kinetic energy. "Low frequency" for matter waves also correlates with low energy. Circular motion is irrelevant to maximizing intrinsic translational kinetic energy.

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