Question

In nuclear fission, $0.1\%$ mass is converted into energy. The energy released in the fission of $1kg$ mass in $kWh$ is
$\begin{aligned} & \text{A}\text{. 2}\text{.5}\times \text{1}{{\text{0}}^{5}} \\\ & \text{B}\text{. 2}\text{.5}\times \text{1}{{\text{0}}^{7}} \\\ & \text{C}\text{. 2}\text{.5}\times \text{1}{{\text{0}}^{9}} \\\ & \text{D}\text{. 2}\text{.5}\times \text{1}{{\text{0}}^{-7}} \\\ \end{aligned}$

Answer 1

Using Einstein’s mass energy relation first calculate the energy released due to the $0.1\%$ of the $1kg$ mass. This is the energy released in one second. Calculate the energy released per hour. Which will give the power released in one hour in terms of watt hour. Convert the energy released per hour to kilowatt hour to get the required answer.

Formulas Used:
Energy equivalent to mass $m$ is given by the Einstein’s mass energy equation and is given by $E=m{{c}^{2}}$
Where, $c$ is the velocity of light and its value is $c=3\times {{10}^{8}}m{{s}^{-1}}$

Complete step by step answer:
Given that $0.1\%$ mass is converted into energy during nuclear fission. Then the amount of mass converted to energy when $1kg$ of mass undergo fission is
$m=\dfrac{0.1}{100}\times 1kg=0.0001kg$
The energy equivalent to this mass is given by Einstein’s mass-energy formula. So the energy equivalent to this mass $m=0.0001kg$ in Joule is
$E=m{{c}^{2}}=0.0001kg\times {{\left( 3\times {{10}^{8}} \right)}^{2}}=9\times {{10}^{13}}J$
Let this energy be released per second.
So the energy released per hour will be
$\begin{aligned} & E'=\dfrac{E}{1hour}=\dfrac{9\times {{10}^{13}}J}{3600s}=0.0025\times {{10}^{13}}watt-hour=2.5\times {{10}^{10}}watt-hour \\\ & \Rightarrow E'=\dfrac{2.5\times {{10}^{10}}}{{{10}^{3}}}kilowatt-hour=2.5\times {{10}^{7}}kWh \\\ \end{aligned}$
So the correct option is $\text{B}\text{. 2}\text{.5}\times \text{1}{{\text{0}}^{7}}$.

Note:
Nuclear fission is the process in which a heavy unstable nucleus breaks into lighter and smaller nuclei. In nuclear fission the heavy nucleus is called the parent nucleus and the smaller nuclei are called daughter nuclei. The mass of the parent nucleus is more than the sum of the masses of the daughter nucleus. This mass difference is converted to energy by the mass energy relation. Nuclear fusion is a spontaneous process and it does not depend upon external factors like temperature, pressure, etc.
Another nuclear process is called nuclear Fusion. In this process two lighter nuclei fuse together to form a bigger nucleus. In this process a huge amount of energy will be released. But a huge amount of energy is required to fuse the nucleus. So nuclear fusion is not possible on earth. Our sun is powered by nuclear fusion. In the sun two Hydrogen fuse together to form Helium. In this process a huge amount of energy is released which powers the sun.