Chapter 27, Problem 54A

To determine

To Find: The velocity of an electron.

Answer to Problem 54A

  $2.43\times {10}^6\text{m/s}$

Explanation of Solution

Given data:

de Broglie wavelength of an electron is $\lambda =3.0\times {10}^{-10}\text{m}$ .

Formula used:

de Broglie equation is:

  $\lambda =\frac{h}{mv}$

  $\lambda =$ de Broglie wavelength

  $h=$ Planck’s constant $=6.626\times {10}^{-34}\text{J}\cdot \text{s}$

m = mass

v = velocity

Calculation:

Substitute the values and solve for v:

  $\lambda =\frac{h}{mv}$

  $3\times {10}^{-10}=\frac{6.63\times {10}^{-34}}{9.1\times {10}^{-31}\times v}$

  $\begin{array}{l}3\times {10}^{-10}\times 9.11\times {10}^{-31}\times v=6.626\times {10}^{-34}\\ v=\frac{6.626\times {10}^{-34}}{27.33\times {10}^{-10}\times {10}^{-31}}\\ v=2.43\times {10}^6\text{m/s}\end{array}$

Conclusion:

Thus, the velocity of the electron is $2.43\times {10}^6\text{m/s}$ .