The total energy released if 47 g of ²³⁵U undergoes fission (disintegration energy per event, Q = 200 MeV, Avogadro's number = 6.02 × 10²³ nuclei/mol) is close to:

Concept:

• Avogadro's Number:
  • ​Avogadro’s number tells us the number of particles in 1 mole (or mol) of a substance.
  • These particles could be electrons or molecules or atoms.
  • The value of Avogadro’s number is approximately 6.02 × 1023 nuclei/mol.
• ​The number of nuclei in a given mass can be calculated by the formula, \(N=\frac{N_A}{M_o} m\) where N_A = Avogadro's number, m = given mass, M_o = molecular mass
• The formula of the total energy is given by, E = NQ where Q = disintegration energy per unit event, N = number of nuclei.
• 1 MeV = 1.6 ×10^-13 J

Explanation:

Given,

The disintegration energy per event, Q = 200 MeV

Avogadro's number, N_A = 6.02 × 1023 nuclei/mol

Given mass, m = 47 g 

The number of nuclei in 47 g of  235U is given by,

\(N=\frac{N_A}{M_o} m\)

\(N=\frac{6.02× 10^{23}}{235} × 47\)

N = 1.204 × 10²³ 

Now, the total energy released is given by, E = NQ

E = 1.204 × 1023 × 200 × 10⁶ ×1.6 ×10^-19

E = 3.85 × 10¹² J

Hence, the energy released is 3.85 × 10¹² J.