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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.)
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Solution
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"`
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