Question

In our universe, the rest energy of an electron is approximately$\mathbf{8}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{14}}\mathit{J}$. What would it be in the alternate universe?
(a)$\mathbf{8}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{8}}\mathit{J}$; (b)$\mathbf{8}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{26}}\mathit{J}$; (c)$\mathbf{8}\mathbf{.}\mathbf{2}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{2}}\mathit{J}$; (d) 0.82J.

Short answer

The energy is$8.2\times {10}^{-26}J$ .Hence, B is the correct option.

Step-by-step solution

Important Concepts

Rest energy of an object is given by

$\mathit{E}\mathbf{=}\mathit{m}{\mathit{c}}^{\mathbf{2}}$

Where m is the rest mass and c is speed of light.

Application

The rest energy of the object is given by

$E=m{c}^2$

Where is the speed of light in alternate universe.

Multiply and divide by the speed of light get,

$E=m{c}^2{\left(\frac{c}{c}\right)}^2$

We know that$E=m{c}^2=8.2\times {10}^{-14}J$

Input these values we get

$$\begin{gathered} E=\left(8.2\times {10}^{-14}J\right){\left(\frac{300m/s}{3\times {10}^{8}m/s}\right)}^2 \\ E=8.2\times {10}^{-26}J \end{gathered}$$

Therefore, the energy is$8.2\times {10}^{-26}J$ .Hence, B is the correct option.