Calculate the wavelength of an electron moving with a velocity of$2.05\times10^7 m s^{–1}$

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Calculate the wavelength of an electron moving with a velocity of $2.05\times10^7 m s^{-1}$

CBSE | Chemistry | Class 11 | NCERT | Structure of Atom

Calculate the wavelength of an electron moving with a velocity of $2.05\times10^7 m s^{-1}$

As per de Broglie’s equation,

$\lambda=\frac{h}{m v}$
Where, $\lambda$ denotes thr wavelength of the moving particle
$\mathrm{m}$ is the mass of the particle
$v$ denotes the velocity of the particle
$\mathrm{h}$ is Planck’s constant
Substituting these values in the expression for $\lambda$ :
$\begin{array}{l} \lambda=\frac{\left(6.626 \times 10^{-34}\right) J_{s}}{\left(9.10939 \times 10^{-31} \mathrm{~kg}\right)\left(2.05 \times 10^{7} \mathrm{~ms}^{-1}\right)} \\ =3.548 \times 10^{-11} \mathrm{~m} \end{array}$
Therefore, the wavelength associated with the electron which is moving with a velocity of $2.05 \times$
$10^{7} \mathrm{~ms}^{-1} \text { is } 3.548 \times 10^{-11} \mathrm{~m}$