Question

The binding energy of helium nucleus is $28\,MeV$ What is its average binding energy per nucleon
A. 102 MeV
B. 56 MeV
C. 14 MeV
D. 7 MeV

Answer 1

in order to solve the question, we will first find the atomic mass of helium use its relation with neutron and proton and then we will use find the its average binding energy per nucleon of helium using its relationship with binding energy of helium as given in the question and the atomic mass of helium

Formula used:
${\text{average binding energy per nucleon = }}\dfrac{{{\text{binding energy}}}}{{{\text{atomic mass}}}}$
Atomic mass = number of proton + number of neutron

Complete step by step answer:
In the question we are given the binding energy of the helium nucleus and we have to find the average binding energy per nucleon.
Binding energy of helium nucleus = 28 MeV
Helium nucleus consists of two protons and two neutrons
Atomic mass = number of proton + number of neutron
Now we will substitute the values in the above formula,
Atomic mass of helium = 4 u
Helium has six bonds each bond has a binding energy of 4.7 MeV which accounts to a total binding energy of 28 MeV. Now to find the average binding energy per nucleon we will use its relation with binding energy as given in question and the atomic mass
${\text{average binding energy per nucleon = }}\dfrac{{{\text{binding energy}}}}{{{\text{atomic mass}}}}$
Now we will substitute the values in the above formula
${\text{average binding energy per nucleon = }}\dfrac{{28}}{4}Mev$
$\therefore {\text{average binding energy per nucleon = 4 }}Mev$

Hence, the correct option is D.

Note: Many of the students will make the mistake by calculating atomic mass by using sum of electron and neutron as it will also result in the same but because in many cases electron and proton are equal but in some cases they are different so that is we should use the formula as sum of neutron and proton.