Ncert Exercises & Solutions

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

From de Broglie’s equation,
$λ = \frac{h}{mv}$
Given,
Kinetic energy (K.E) of the electron = 3.0 × $10^{- 25}$ J

$Since K . E . = \frac{1}{2} {mv}^{2}$
$∴ Velocity (v) = \sqrt{\frac{2 K . E .}{m}}$
$= \sqrt{\frac{2 (3.0 x 10^{- 25} J)}{9.10939 x 10^{- 31} kg}}$
$= \sqrt{6.5866 x 10^{4}}$
$v = 811.579 m / s$

Substituting the value in the expression of λ:
$λ = \frac{6.626 x 10^{- 34} Js}{(9.10939 x 10^{- 31} kg) (811.579 m / s)}$
$λ = 9.9625 x 10^{- 7} m$
Hence, the wavelength of the electron is 8.9625 × $10^{- 7}$ m.

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