Determine the energy, the frequency, and the momentum of an X-ray...

Determine the energy, the frequency, and the momentum of an X-ray photon having a wavelength of

0.10 \text{ nm}

Options

A $12.4 \text{ keV}$ , $3 \times 10^{17} \text{ Hz}$ , $6.62 \times 10^{-23} \text{ kg m s}^{-1}$
B $124 \text{ keV}$ , $3 \times 10^{19} \text{ Hz}$ , $6.62 \times 10^{-23} \text{ kg m s}^{-1}$
C $1.24 \text{ keV}$ , $3 \times 10^{17} \text{ Hz}$ , $6.62 \times 10^{-25} \text{ kg m s}^{-1}$
D $12.4 \text{ keV}$ , $3 \times 10^{18} \text{ Hz}$ , $6.62 \times 10^{-24} \text{ kg m s}^{-1}$

D. $12.4 \text{ keV}$ , $3 \times 10^{18} \text{ Hz}$ , $6.62 \times 10^{-24} \text{ kg m s}^{-1}$

Given wavelength

\lambda = 0.10 \text{ nm} = 10^{-10} \text{ m}

.

The energy of the photon is given by

E = \dfrac{hc}{\lambda}

.

Using

hc \approx 1240 \text{ eV nm}

E = \dfrac{1240 \text{ eV nm}}{0.10 \text{ nm}} = 12400 \text{ eV} = 12.4 \text{ keV}

.

The frequency of the photon is given by

\nu = \dfrac{c}{\lambda}

\nu = \dfrac{3 \times 10^8 \text{ m s}^{-1}}{10^{-10} \text{ m}} = 3 \times 10^{18} \text{ Hz}

.

The momentum of the photon is given by

p = \dfrac{h}{\lambda}

p = \dfrac{6.62 \times 10^{-34} \text{ J s}}{10^{-10} \text{ m}} = 6.62 \times 10^{-24} \text{ kg m s}^{-1}