Question

Calculate the wavelength of helium atom whose speed is equal to its rms speed at ${27}^{0}C$.

• A. $293\times {10}^{-11}m$
• B. $7.29\times {10}^{-11}m$
• C. $123\times {10}^{-11}m$
• D. $133\times {10}^{-10}m$

Answer 1

The correct option is B $7.29\times {10}^{-11}m$

The rms speed is $u=\sqrt{\frac{3RT}{M}}=\sqrt{\frac{3\times 8.314\times 300}{4\times {10}^{-3}}}=1367m/s$.
The mass of He atom is $\frac{4\times {10}^{-3}}{6.023\times {10}^{23}}=6.64\times {10}^{-27}$
The wavelength of He atom is $\lambda =\frac{h}{mu}=\frac{6.6\times {10}^{-34}}{6.64\times {10}^{-27}\times 1367}=7.29\times {10}^{-11}m$