a beam of helium atoms moves with a velocity of 20000 m/s. Find the wavelength of particles constituting with the beam

Dear Student,

Please find below the solution to the asked query:

According to de-Broglie relation: $\lambda =\frac{h}{P}=\frac{h}{mv}$

As 1 mol or 4 g of He contains 6.022 x 10²³ atoms, then mass of single He atom = (4 / 6.022 x 10²³ ) = 6.64 x 10^-24 g

Hence, the wavelength = $$\begin{gathered} \lambda =\frac{h}{mv}=\frac{6.626\times {10}^{-34} Kg m^2{s}^{-1}}{6.64\times {10}^{-27} Kg\times 20000 m{s}^{-1}}=4.99\times {10}^{-12} m \\ \lambda = \mathbf{499}\mathbf{ }\mathit{p}\mathit{m} \end{gathered}$$


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