#### Question

Calculate the mass of an α-particle. Its Its binding energy is 28.2 MeV.

(Use Mass of proton m_{p} = 1.007276 u, Mass of `""_1^1"H"` atom = 1.007825 u, Mass of neutron m_{n} = 1.008665 u, Mass of electron = 0.0005486 u ≈ 511 keV/c^{2},1 u = 931 MeV/c^{2}.)

#### 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, m_{p} = Mass of proton

m_{n} = 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?

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.