The mass of helium atom of mass number 4 is 4.0026 amu, while that of the neutron and proton are 1.0087 and 1.0078 respectively on the same scale. Hence, the nuclear binding energy per nucleon in the helium atom is nearly

Question

The mass of helium atom of mass number 4 is 4.0026 amu, while that of the neutron and proton are 1.0087 and 1.0078 respectively on the same scale. Hence, the nuclear binding energy per nucleon in the helium atom is nearly (A) 5 MeV (B) 7 MeV (C) 10 MeV (D) 14 MeV

Tardigrade Admin · Accepted Answer

He atom has 2p+2n Hence, Δ m=(2× 1.0078+2× 1.0087)-4.0026 =0.0304 amu ∴ energy released =0.0304× 931.5 MeV =28.3 MeV Binding energy per nucleon =(28.3/4)=7 MeV (approximately)

Q. The mass of helium atom of mass number $4$ is $4.0026$ amu, while that of the neutron and proton are $1.0087$ and $1.0078$ respectively on the same scale. Hence, the nuclear binding energy per nucleon in the helium atom is nearly

5 MeV

7 MeV

10 MeV

14 MeV

He atom has $2 p + 2 n$
Hence,
$Δ m = (2 \times 1.0078 + 2 \times 1.0087) - 4.0026$
$= 0.0304 am u$
$∴$ energy released
$= 0.0304 \times 931.5 M e V$
$= 28.3 M e V$
Binding energy per nucleon
$= \frac{28.3}{4} = 7 M e V$ (approximately)

Q. The mass of helium atom of mass number 4 is 4.0026 amu, while that of the neutron and proton are 1.0087 and 1.0078 respectively on the same scale. Hence, the nuclear binding energy per nucleon in the helium atom is nearly