For what kinetic energy of a neutron will the associated de-Broglie wavelength be 1.40 x 10^–10 m?

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Solution

De-broglie wavelength,

λ

1.40 \times 10^{- 10} m

Mass of neutron, m = 1.675 \times 10^{- 27} kg Planck' s constant, h = 6.63 \times 10^{- 34} Js De - brogliw wavelength is given by, λ = \frac{h}{mv}

i . e ., v = \frac{h}{mλ} \Rightarrow v = \frac{6.63 \times 10^{- 34}}{1.675 \times 10^{- 27} \times 1.40 \times 10^{- 10}} = 28.28 \times 10^{2} m / s

Kinetic energy is given by, K.E =

\frac{1}{2} m v^{2}

= \frac{1}{2} \times 1.675 \times 10^{- 27} \times (28.8 \times 10^{2})^{2} = 6.634 \times 10^{- 21} J

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