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Question
Calculate the mass of an α-particle. Its Its binding energy is 28.2 MeV.
(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
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Solution
Given:-
Binding energy of α particle = 28.2 MeV
Let x be the mass of α particle.
We know an α particle consists of 2 protons and 2 neutrons.
Binding energy ,
`B = (Zm_p + Nm_n - M)c^2`
Here, mp = Mass of proton
mn = Mass of neutron
Z= Number of protons
N = Number of neutrons
c = Speed of light
On substituting the respective values, we have
`28.2 = (2 xx 1.007276 + 2 xx 1.008665 - x)c^2`
`⇒ x = 4.0016 "u"`
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(Use Mass of proton mp = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron mn = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c2,1 u = 931 MeV/c2.)
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