Question

In each fission of ${}_{92}{U}^{235}$ releases $200MeV$, how many fissions must occur per second to produce power of $1kW$?

• A. $1.25\times {10}^{18}$
• B. $3.125\times {10}^{13}$
• C. $3.2\times {10}^{18}$
• D. $1.25\times {10}^{13}$

Answer 1

The correct option is B $3.125\times {10}^{13}$

Let $n$ be number of fissions per second.
Each fission produces 200 MeV.
$n\times 200\times {10}^6$ eV is produced in one second by n fissions
But 1 eV $=1.6\times {10}^{-19}$ J
Hence, power produced $=n\times 200\times {10}^6\times 1.6\times {10}^{-19}$ Joule per second.
Also 1 J/s $=$ 1 W and
1000 J/s $=$ 1 kW.
The required power is 1 kW.

Hence, $\frac{n\times 200\times {10}^6\times 1.6\times {10}^{-19}}{{10}^3}=1$
$n=\frac{{10}^3}{2\times 1.6\times {10}^{-11}}=\frac{{10}^{14}}{3.2}$

$=\frac{10}{3.2}\times {10}^{13}=3.125\times {10}^{13}$