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**De-Broglie wavelength of particle passing through a potential**

The De-Broglie wavelength is the wavelength $λ$, associated with a object and is related to its momentum and mass.

The De-Broglie relation for a particle is given by,

$λ=ph $

or $λ=mvh $

where, $λ$ is wavelength

h is plank's constant

p is momentum

m is mass

v is speed

Consider an electron (mass m, charge e) accelerated from rest through a potential V. The kinetic energy K of the electron equals the work done (eV ) on it by the electric field: K = eV

Now, $K=1/2mv_{2}=p_{2}/2m$

so that, $p=(2mK)_{1/2}$

$p=(2meV)_{1/2}$

The De-Broglie wavelength is given by,

$λ=h/(2meV)_{1/2}$

Substituting the numerical values of h, m, e, we get

$λ=1.227/(V)_{1/2}$ nm

where V is the magnitude of accelerating potential in volts.

For a 120 V accelerating potential, $λ=0.112$ nm.

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de Broglie Wavelength

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