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Calculate the Mass of an α-particle. Its Its Binding Energy is 28.2 Mev. - Physics

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ConceptMass-energy and Nuclear Binding Energy Mass - Energy

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.)

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"`

  Is there an error in this question or solution?

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Solution Calculate the Mass of an α-particle. Its Its Binding Energy is 28.2 Mev. Concept: Mass-energy and Nuclear Binding Energy - Mass - Energy.
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