The mass of an electron is 9.1 × 10–31 kg. If its K.E. is 3.0 × 10–25 J, calculate its wavelength.

Asked by Abhisek | 1 year ago |  120

##### Solution :-

As per de Broglie’s equation,

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

Given, K.E of electron =$$3.0\times 10^{-25}J$$

Since K.E.=$$\dfrac{1}{2}mv^{2}$$

$$∴ Velocity(v)=\sqrt{\dfrac{2K.E}{m}}\\ \\$$

$$=\sqrt{\dfrac{2(3.0\times 10^{-25}J)}{9.10939\times 10^{-31}kg}}\\ \\$$

$$=\sqrt{6.5866\times 10^{4}}\\ \\ v=811.579\, ms^{-1}$$

Substituting these values in the expression for λ:

$$\lambda =\dfrac{(6.626\times 10^{-34})Js}{(9.10939\times 10^{-31}kg)(811.579ms^{-1})}\\ \\$$

$$=8.9625\times 10^{-7}\, m= 8967 Å$$

Answered by Abhisek | 1 year ago

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