Question

An electron is accelerated through a potential difference of 10,000V. Its de Broglie
wavelength is, (nearly):
\[({{m}_{e}}=9\times {{10}^{-31}}kg)\]
A.. \[12.2\times {{10}^{-13}}m\]
B. \[12.2\times {{10}^{-12}}m\]
C. \[12.2\times {{10}^{-14}}m\]
D. \[12.2nm\]

Answer 1

Hint: As per wave-molecule duality, the De Broglie frequency is a frequency shown in all the objects in quantum mechanics which decides the likelihood density of finding the object at a given purpose of the setup space. The de Broglie frequency of a molecule is contrarily relative to its momentum.

Complete step-by-step answer:
The correct answer is B.
 de-Broglie wavelength is given by \[\lambda =\dfrac{h}{p}\]

\[=\dfrac{12.27\times {{10}^{-10}}}{\sqrt{10000}}\]

\[=12.27\times {{10}^{-12}}m\]

At the point when particles are energized by different particles over the span of the examination or during the collision of particles with estimating instruments, inner standing waves can happen in the particles.

They can be electromagnetic waves or waves related to the solid collaboration of particles, with solid, attractive energy in the gravitational model of solid association, and so on. With the assistance of Lorentz changes, we can decipher the frequency of these inner motions into the frequency identified by an outer onlooker, directing the analysis with moving particles.

Also, since the de Broglie frequency carries on like the photon frequency with the related momentum, which joins particles and waves, de Broglie frequencies are viewed as likelihood waves related to the wave work. In quantum mechanics, it is accepted that the squared sufficiency of the wave work at a given point in the facilitated portrayal decides the likelihood density of finding the molecule now.

Note: The electromagnetic potential of particles diminishes in the reverse extent of the good ways from the molecule to the perception point, the potential of solid collaboration in the gravitational examples of solid communication acts in a similar way. At the point when inside motions start in the molecule, the field potential around the molecule begins swaying as well, and therefore, the adequacy of the de Broglie frequency is developing quickly while moving toward the molecule.

This compares accurately to the way that the molecule in all probability is at the spot, where the playfulness of its wave work is the best. For this situation, the wave capacity would make more probable mirror the complete abundance of the joined de Broglie wave, related with the all-out playfulness of the consolidated wave field of the particles' potentials.