Chapter 27.1, Problem 6PP

To determine

To Calculate: Velocity of the electron.

Answer to Problem 6PP

Velocity of the electron is, $v=9.0\times {10}^5\text{ m/s}$

Explanation of Solution

Given data:

Energy of electron is 2.3 eV

Formula Used:

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

Here, m is the mass and v is the velocity.

Calculation:

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

  $KE=\left(2.3\text{ eV}\right)\left(\frac{1.60\times {10}^{-19}\text{ J}}{1\text{ eV}}\right)=3.7\times {10}^{-19}\text{J}$

Therefore, velocity of the electron can be calculated as,

  $\begin{array}{l}\text{K}\text{.E}=\frac{1}{2}m{v}^2\\ v=\sqrt{\frac{2KE}{m}}\\ v=\sqrt{\frac{2\left(3.7\times {10}^{-19}\text{ J}\right)}{9.1\times {10}^{-31}\text{kg}}}\\ v=9.0\times {10}^5\text{ m/s}\end{array}$

Conclusion:

Therefore, velocity of the electron is, $v=9.0\times {10}^5\text{ m/s}$