Question

An atomic power nuclear reactor can deliver $300MW$. The energy released due to the fission of each nucleus of the uranium atom $U^{238}$ is $170MeV$. The number of uranium atoms fissioned per hour will be:

Answer 1

Step 1: Given data

1. The power generated by the reactor is $P=300MW$.
2. The amount of energy produces is $E=170MeV$.
3. The time taken by the reactor is $t=3600seconds.$

Step 2: Understand Nuclear fission

1. Nuclear fission is the process that brokes heavy atoms into smaller parts.
2. The power generated by nuclear is given by the form, $P=\frac{E\times n}{t}$, where $\mathrm{E}$ is the amount of energy produced in time $\mathrm{t}$ and $\mathrm{n}$ is the number of the nucleus.

Step 3: Find the number of atoms

Let $\mathrm{n}$ be the number of atoms fissioned per hour.

As we know, power generated by nuclear is $P=\frac{E\cdot n}{t}$.

So,

$$\begin{gathered} \frac{n}{t}=\frac{P}{E}=\frac{300MW}{170MeV}=\frac{300\times {10}^6}{170\times 1.6\times {10}^{-13}}\left(\sin ce,1MeV=1.6\times {10}^{-13}joule\right) \\ orn=\left(1.103\times {10}^{19}\right)\times t \\ orn=\left(1.103\times {10}^{19}\right)\times 3600 \\ orn=3.970\times {10}^{22} \end{gathered}$$

Therefore, the number of uranium atoms fissioned per hour is $n=3.970\times {10}^{22}$.