High School

The binding energy per nucleon of [tex]^{10}X[/tex] is 9 MeV, and that of [tex]^{11}X[/tex] is 7.5 MeV, where X represents an element.

What is the minimum energy required to remove a neutron from [tex]^{11}X[/tex]?

(a) 7.5 MeV
(b) 2.5 MeV
(c) 8 MeV
(d) 0.5 MeV

Answer :

Final answer:

The minimum energy required to remove a neutron from an element is equal to the difference in binding energies per nucleon between the element with the neutron and the element without the neutron.Thus option

(d) 0.5 MeV is the correct answer for the above question.

Explanation:

The minimum energy required to remove a neutron from an element is equal to the difference in binding energies per nucleon between the element with the neutron and the element without the neutron. In this case, the binding energy per nucleon for 10X is 9 MeV and for 11X is 7.5 MeV. Therefore, the minimum energy required to remove a neutron from 11X would be:



Minimum energy = Binding energy per nucleon of 10X - Binding energy per nucleon of 11X



Minimum energy = 9 MeV - 7.5 MeV = 1.5 MeV



So, the correct answer is (d) 0.5 MeV.