Chapter 27, Problem 62A

To determine

To Compare: The de Broglie wavelength and diameter of the given baseball.

Explanation of Solution

Given data:

Diameter of baseball, $d=0.10\text{m}$

Velocity of the baseball, $v=21\text{m/s}$

Average mass of baseball, $m=145\text{g}=0.145\text{kg}$

Formula used:

de Broglie wavelength of the baseball can be obtained by:

  $\lambda =\frac{h}{mv}$

Here, h is the Planck’s constant, m is the mass and v is the velocity of the baseball.

Calculation:

de Broglie wavelength of the baseball:

  $\begin{array}{c}\lambda =\frac{h}{mv}\\ =\frac{6.6\times {10}^{-34}}{0.145\times 21}\\ =2.17\times {10}^{-34}\text{m}\end{array}$

The ratio of de Broglie wavelength of the baseball and its diameter is:

  $\frac{\lambda }{d}=\frac{2.17\times {10}^{-34}\text{m}}{0.10\text{m}}=2.17\times {10}^{-33}$

Conclusion:

The de-Broglie wavelength is $2.17\times {10}^{-33}$ times the diameter of the baseball.