Chapter 27, Problem 66A

To determine

To Find: de Broglie wavelength of a deuteron.

Answer to Problem 66A

  $8.03\times {10}^{-12}\text{m}$

Explanation of Solution

Given data:

Mass of deuteron, $m=3.3\times {10}^{-27}\text{kg}$

Speed of deuteron, $v=\text{2}\text{.5}\times {\text{10}}^4\text{m/s}$

Formula used:

de Broglie wavelength

  $\lambda =\frac{h}{mv}$

Here, h is the Planck’s constant.

Calculation:

Substitute the values and solve:

  $\begin{array}{l}\lambda =\frac{6.626\times {10}^{-34}\text{J}\cdot \text{s}}{3.3\times {10}^{-27}\text{kg}\times 2.5\times {10}^4\text{m/s}}\\ \lambda =8.03\times {10}^{-12}\text{m}\end{array}$

Conclusion:

Hence, the de Broglie wavelength of the deuteron is $8.03\times {10}^{-12}\text{m}$ .