Question

How do You find the Speed of an Electron?

Answer 1

To find the speed of an electron:

1. An atom consist of electron, proton and neutron. The electron is one the subatomic particle having mass $9\times {10}^{-31}\mathrm{kg}.$ Every moving object has kinetic energy which is equal to $1/2{\mathrm{mv}}^2$, here $\mathrm{m}=\mathrm{mass}\mathrm{of}\mathrm{the}\mathrm{object}\mathrm{and}\mathrm{v}=\mathrm{velocity}$.
2. The equation is in electromagnetics, $\mathrm{qV}=1/2{\mathrm{mv}}^2,\mathrm{where}\mathrm{m}=9\times {10}^{-31}\mathrm{kg}\mathrm{and}\mathrm{q}=\mathrm{the}\mathrm{charge}\mathrm{of}\mathrm{a}\mathrm{single}\mathrm{electron}(1.6\times {10}^{-19}\mathrm{C})$
3. Speed of electron $\mathrm{V}=1/2{\mathrm{mqv}}^2$​​
4. For example, Find the speed of electron when $\mathrm{V}=100$?

Step 1: $v=\sqrt{2qV/m}$

Step 2: Given: $\mathrm{m}=9\times {10}^{-31}\mathrm{kg}$,$\mathrm{q}=1.6\times {10}^{-19}\mathrm{C}$,$\mathrm{v}=100$

$$\begin{gathered} v=\sqrt{2qV/m} \\ v=\sqrt{2\times 1.6\times {10}^{-19}\times 100/9\times {10}^{-31}} \\ v=6\times {10}^{6}m/s \end{gathered}$$

Thus, the speed of electron is calculated by $v=\sqrt{2qV/m}$