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 mv^{2} = 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 10^{34} kg-m/s

m = 9. 7 x 10^{31} kg

e = 1.6 x 10^{19}coulomb

**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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