An electron and a photon each have a wavelength of $1.00$ nm. Find the kinetic energy of the electron.

Home » An electron and a photon each have a wavelength of nm. Find the kinetic energy of the electron.

An electron and a photon each have a wavelength of $1.00$ nm. Find the kinetic energy of the electron.

Wavelength of an electron is represented by $\lambda_{e}$ and that of a photon by $\lambda_{p}$ ,

So,

$\lambda_{e}=\lambda_{p}=\lambda=1 \mathrm{~nm}=1 \times 10^{-9} \mathrm{~m}$

Planck’s constant, $h=6.63 \times 10^{-34} \mathrm{~J} \mathrm{~s}$

For an electron having momentum $p$ , the kinetic energy (K) is given by the relation:

$\mathrm{K}=\frac{1}{2} \frac{p^{2}}{m}$

Where, $m=$ Mass of the electron $=9.1 \times 10^{-31} \mathrm{Kg}$

$p=6.63 \times 10^{-25} \mathrm{Kg} \mathrm{m} / \mathrm{s}$

Therefore, $\mathrm{K}=\frac{1}{2} \times \frac{\left(6.63 \times 10^{-25}\right)^{2}}{9.1 \times 10^{-31}}$

$=2.415 \times 10^{-19} \mathrm{~J}$

$=\frac{2.415 \times 10^{-19}}{1.6 \times 10^{-19}}=1.51 \mathrm{eV}$

The kinetic energy of the electron is $1.51 \mathrm{eV}$ .

i

Sign up now and study all subjects for free