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  • The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (a) an electron would have the same de Broglie wavelength.

Q: 11.14 (a) The wavelength of light from the spectral emission line of sodium is 589\hspace{1mm}nm. Find the kinetic energy at which an electron would have the same de Broglie wavelength. 

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The momentum of a particle with de Broglie wavelength of 589 nm is

\\p=\frac{h}{\lambda }\\ p=\frac{6.62\times 10^{-34}}{589\times 10^{-9}}\\ p=1.12\times 10^{-27}\ kg\ m\ s^{-1}

The Kinetic Energy of an electron moving with above-mentioned momentum is

\\K=\frac{p^{2}}{2m_{e}}\\ K=\frac{(1.12\times 10^{-27})^{2}}{2\times 9.1\times 10^{-31}}\\ K=6.89\times 10^{-25}\ J

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