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For an Electron Passing Through Potential Difference V, Show that Its Wavelength Is; λ = 12.26/√V A°. - Applied Physics 1

Answer in Brief

For an electron passing through potential difference V, show that its
wavelength is; 

λ = 12.26/√V A°.

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Solution

The wavelength of an electron with kinetic energy E is given by
λ = h/√2mE ............................ (1)

On the other hand, the kinetic energy of an electron passing through potential difference'V' is,
1/2 mv2  = eV

Hence, E=eV Thus, replacing E with eV in equation (1), we get,
λ =h √2meV ............................ (2)

Substituting values of,
h = 6.63 x 1034 kg-m/s
m = 9. 7 x 1031 kg
e = 1.6 x 1019coulomb

in equation (2), we get,
λ= 1.226 x 10-19/√V metre
λ = 72.26 /√V A°

Concept: De Broglie Wavelength
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