Question

What is binding energy per nucleon ? Explain with the help of diagram how binding energy per nucleon affects nuclear stability ?

Answer 1

i. Binding energy per nucleon (\(\bar B\)), for nucleus containing (A) nucleons with binding energy (B.E.) is given as,

\(\bar B\) = B.E./A

ii. Mean binding energy per nucleon (\(\bar B\)) for the most stable isotopes as a function of mass number is shown above. This plot leads to the following inferences :

a. Light nuclides : 

(A < 30)

The peaks with A values in multiples of 4. 

For example,

\(_2^4He\), \(_6^{12}C\),\(_8^{16}O\) are more stable.

b. Medium mass nuclides : 

(30 < A < 90)

\(\bar B\) increases typically from 8 MeV for A = 16 to nearly 8.3 MeV for A between 28 and 32 and it remains nearly constant 8.5 MeV beyond this and shows a broad maximum. The nuclides falling on the maximum are most stable which turns possess high values. ⁵⁶Fe with \(\bar B\) value of 8.79 MeV is the most stable.

c. Heavy nuclides : 

(A > 90)

\(\bar B\) decreases from maximum 8.79 MeV to 7.7 MeV for A ≅ 210, 209Bi is the stable nuclide. Beyond this, all nuclides are radioactive (αemitters).