Question

The energy released when one nucleus of ${}_{92}{U}^{235}$ undergoes fission is $188MeV$. The energy released when $100g$ of ${}_{92}{U}^{235}$ undergoes fission is

• A. $3.55\times 10^{12}J$
• B. $7.71\times 10^{12}J$
• C. $3.55\times 10^{13}J$
• D. $7.71\times 10^{13}J$

Answer 1

Answer: (B)

Given, energy released, $E_0=188MeV$ per nucleus fission and mass, $m=100gm$
As number of nucleus in $100gm$ of ${}_{92}{U}^{235}$
$N=\frac{100}{M}\times N_A$
where, $N_A=$ Avogadro number and
$M$ = molecular mass
$\Rightarrow N=\frac{100}{235}\times 6.022\times 10^{23}=2\cdot 56\times 10^{23}$ nucleus
Energy released in fission of one nucleus
$E_0^{\prime }=E_0=188\times 10^6\times 1.6\times 10^{-19}J$
$=300.8\times 10^{-13}J$
So, Energy released in N-nucleus fission,
$E=E_0^{\prime }N=2\cdot 5610^{23}\times 300.8\times 10^{-13}J$
$\Rightarrow E=7.71\times 10^{12}J$