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Question
When a photon is emitted by a hydrogen atom, the photon carries a momentum with it. (a) Calculate the momentum carries by the photon when a hydrogen atom emits light of wavelength 656.3 nm. (b) With what speed does the atom recoil during this transition? Take the mass of the hydrogen atom = 1.67 × 10−27 kg. (c) Find the kinetic energy of recoil of the atom.
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Solution
Given:
Wavelength of light emitted by hydrogen, λ = 656.3 nm
Mass of hydrogen atom, m = 1.67 × 10−27 kg
(a) Momentum (P) is given by
P =`h/lamda`
Here,
h = Planck's constant
λ = Wavelength of light
`therefore p = (6.63xx10^-34)/(656.3 xx 10^-9)`
p = 0.01×10-25
p =1 × 10-27 kgm/s
(b) Momentum, p = mv
Here,
m = Mass of hydrogen atom
v = Speed of atom
`therefore 1xx10^-27 = (1.67xx10^-27)xxU`
`rArr v = 1/1.67 = 0.598 = 0.6 m/s`
(c) Kinetic energy (K) of the recoil of the atom is given by
`K = 1/2mv^2`
Here,
m = Mass of the atom
v = Velocity of the atom
`therefore K = 1/2 xx (1.67xx10^-27)xx(0.6)^2 J`
`K = (0.3006xx10^-27)/(1.6xx10^-19)eV`
`K = 1.9 xx 10^-9 ev`
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