Question

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

Answer 1

Hint:The nuclear fission is the process in which the uranium atom breaks into smaller parts and releases the energy. We can use this energy for the destruction purposes as for the bomb making and also for the generation of electricity.

Formula used:The formula of the power developed by the nuclear reactor is given by $P = \dfrac{{E \cdot n}}{t}$ where P is the power n is the number of atoms t is the time taken and E is the energy.

Complete step by step answer:
It is given that an atomic power nuclear reactor can deliver 300 MW and the energy released by each nucleus is equal to 170 MeV and we need to calculate the number of uranium atoms fissioned per hour.
As the power of the nuclear reactor is given by,
$P = \dfrac{{E \cdot n}}{t}$
Where P is the power n is the number of atoms t is the time taken and E is the energy. The number of uranium atoms per second fissioned is equal to,
$ \Rightarrow P = \dfrac{{E \cdot n}}{t}$
$ \Rightarrow \dfrac{n}{t} = \dfrac{P}{E}$
The value of the power is 300 MW and the energy is given as 170MeV.
$ \Rightarrow \dfrac{n}{t} = \dfrac{P}{E}$
Replacing the value of P and E in the above relation we get,
$ \Rightarrow \dfrac{n}{t} = \dfrac{{300}}{{170 MeV}}$
As $1MeV = 1 \cdot 6 \times {10^{ - 13}}$ therefore we get,
$ \Rightarrow \dfrac{n}{t} = \dfrac{{300}}{{170 \times 1.6 \times {{10}^{ - 13}}}}$
$ \Rightarrow \dfrac{n}{t} = 1 \cdot 102 \times {10^{19}}$
This is the number of uranium atoms per second. Let us calculate the value of the number of uranium atoms per hour.
$ \Rightarrow \dfrac{n}{t} = 1 \cdot 102 \times {10^{19}} \times 3600$
$ \Rightarrow \dfrac{n}{t} = 3 \cdot 97 \times {10^{22}}$
$ \Rightarrow \dfrac{n}{t} \approx 4 \times {10^{22}}$
So the number of uranium atoms per hour being fissioned is equal to $4 \times {10^{22}}$.

Note:The power delivered by the nuclear power plant is very high as compared to a coal based power plant as the energy released by the nuclear fission per kilograms of uranium is far more than the energy released per kilograms of coal.