Chapter 27, Problem 6STP

To determine

To Choose: The correct option.

Answer to Problem 6STP

Option D

Explanation of Solution

Given data:

Velocity of electron $=391\text{km/s}$ or $391\times {10}^3\text{m/s}$

Mass of electron $=9.11\times {10}^{-31}\text{kg}$

Formula used:

de Broglie wavelength $(\lambda )$ :

  $\lambda =\frac{h}{mv}$

Where,

  $\lambda =$ de Broglie wavelength

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

  $m=$ mass of electron

  $v=$velocity of electron

Calculation:

Substitute the values and solve:

  $\lambda =\frac{h}{mv}$

  $\begin{array}{l}\lambda \text{ =}\frac{6.626\times {10}^{-34}}{9.11\times {10}^{-31}\times 391000}\\ \lambda =1.86\times {10}^{-9}\text{m}\end{array}$

Conclusion:

Thus, the de Broglie wavelength of the electron is $1.86\times {10}^{-9}\text{m}$ . Option D is correct.