Chapter 27.1, Problem 7PP

To determine

To calculate: kinetic energy of electron in eV .

Answer to Problem 7PP

Kinetic energy of electron in eV is, $\text{K}\text{.E}=109.6\text{ eV}$ .

Explanation of Solution

Given:

Velocity, $v=6.2\times {10}^6\text{ m/s}$

Formula:

  $\text{K}\text{.E}=\frac{1}{2}m{v}^2$

Calculation:

Mass of electron is, $m_e=9.1\times {10}^{-31}\text{ kg}$

  $\begin{array}{l}\text{K}\text{.E}=\frac{1}{2}m{v}^2\\ \text{K}\text{.E}=\frac{1}{2}\times 9.1\times {10}^{-31}\times {\left(6.2\times {10}^6\right)}^2\\ \text{K}\text{.E}=\frac{1}{2}\times 9.1\times {10}^{-31}\times 38.44\times {10}^{12}\\ \text{K}\text{.E}=\frac{1}{2}\times 349.8\times {10}^{-19}\\ \text{K}\text{.E}=174.9\times {10}^{-19}\text{ J}\end{array}$

Since, $1\text{ eV}=1.6\times {10}^{-19}\text{ J}$

Therefore, kinetic energy in eV can be calculated as,

  $\begin{array}{l}\text{K}\text{.E}=174.9\times {10}^{-19}\text{ J}\\ \text{K}\text{.E}=\frac{174.9\times {10}^{-19}}{1.6\times {10}^{-19}}\\ \text{K}\text{.E}=109.3\text{ eV}\end{array}$

Conclusion:

Therefore, kinetic energy of electron in eV is, $\text{K}\text{.E}=109.3\text{ eV}$ .