Question

Represent the variation of binding energy per nucleon with mass number. On the basis of it, explain the following: (i) Nuclear fission
(ii) Nuclear fusion
(iii) Nuclear energy

Hint:

Nuclear fusion occurs in stars, while nuclear fission is used in power plants.

Answer 1

Step 1: The binding energy per nucleon varies with mass number. 

Step 2: The curve shows that lighter nuclei and very heavy nuclei have lower binding energy, while medium-sized nuclei (e.g., iron) have the highest binding energy, making them more stable. \[ \boxed{\text{Most stable nucleus: } \text{Fe (A = 56)}} \] 

(i) Nuclear Fission

Solution: 
Nuclear fission is the process where a heavy nucleus splits into smaller nuclei, releasing energy.
Step 1: Heavy elements such as uranium-235 split into lighter elements when bombarded with neutrons. 

Step 2: This process releases energy due to the increase in binding energy per nucleon. \[ \boxed{\text{Heavy nucleus } \rightarrow \text{ Two lighter nuclei } + \text{ Energy}} \] 

(ii) Nuclear Fusion 

Solution:  Nuclear fusion is the process where lighter nuclei combine to form a heavier nucleus, releasing energy.
Step 1: Light elements such as hydrogen nuclei fuse together under high temperature and pressure to form helium. 

Step 2: This results in a release of energy due to an increase in binding energy per nucleon. \[ \boxed{\text{Light nuclei } \rightarrow \text{ Heavier nucleus } + \text{ Energy}} \] 

(iii) Nuclear Energy 

 Solution: Nuclear energy is the energy released during fission or fusion due to changes in binding energy.
Step 1: The energy released during fission and fusion reactions is calculated using Einstein's equation: \[ E = mc^2 \] Step 2: This energy is harnessed in nuclear reactors and stars. \[ \boxed{\text{Energy is released due to mass defect.}} \]