#### 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 × 10^{8} m/s.)

#### Solution

Given:

Wavelength of the X-ray photon, *λ *= 0.1 nm

Speed of light, *c* = 3 `xx` 10^{8} 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"`

Is there an error in this question or solution?

#### APPEARS IN

Solution Find the Energy, the Frequency and the Momentum of an X-ray Photon of Wavelength 0.10 Nm. Concept: Electromagnetic Spectrum.