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# The mass of an electron is 9.1 x 10 ^-31 kg If its K.E. is 3.0 x 10^-25 J, calculate its wavelength.

2.21 The mass of an electron is $9.1\times 10^{-31}\ \textup{kg}$ If its K.E. is $3.0\times 10^{-25}\ \textup{J}$, calculate its wavelength.

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The wavelength of an electron can be found by de Broglie's equation:

$\lambda = \frac{h}{mv}$

Given the K.E. of electron $3.0\times 10^{-25}\ \textup{J}$ which is equal to $\frac{1}{2}mv^2$.

Hence we get,

$\frac{1}{2}mv^2 = 3.0\times10^{-25}J$

$v = \sqrt{\frac{2KE}{m}} = \sqrt{\frac{2(3.0\times10^{-25}J)}{9.1\times10^{-31}kg}} = 811.579\ m/s$

Hence the wavelength is given by,

$\lambda = \frac{6.626\times10^{-34}Js}{(9.1\times10^{-31}kg)(811.579\ m/s)}$

$= 8.9625\times10^{-7}m$

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