Question

Find the energy, the frequency and the momentum of an X-ray photon of wavelength 0.10 nm.

(Use Planck constant h = 4.14 × 10^-15 eVs, speed of light c = 3 × 10⁸ m/s.)

Answer 1

Given:
Wavelength of the X-ray photon, λ = 0.1 nm
Speed of light, c = 3 `xx` 10⁸ m/s

(a) Energy of the photon (E) is given by

`E = (hc)/lambda`

⇒ `E = (1242  "eV")/0.1`

⇒ `E = 12420  "eV"`

⇒ `E = 12.42  "keV" ≈ 12.4  "keV"`

(b) Frequency is given by

`v = c/lambda`

⇒`v = (3 xx 10^8)/(0.1 xx 10^-9)`

⇒`v = 3 xx 10^18  "Hz"`

(c) Momentum of the photon (P) is given by

`P = E/c`

⇒`P = (12.4 xx 10^3 xx 1.6 xx 10^-19)/(3 xx 10^8)`

⇒`P = 6.613 xx 10^-24   "kg-m/s" ≈ 6.62 xx 10^-24  "g-m/s"`