Chapter 27.2, Problem 26PP

a.

To determine

To Find: de Broglie wavelength of the bowling ball.

Answer to Problem 26PP

de Broglie wavelength $=1.1\times {10}^{-36}\text{m}$

Explanation of Solution

Given data:

Mass of the bowling ball $=70\text{kg}$

Velocity of the ball $=8.5\text{m/s}$

Formula used:

de Broglie wavelength can be obtained by:

  $\lambda =\frac{h}{mv}$

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

Calculation:

Substitute the values and solve:

  $\begin{array}{l}\lambda =\frac{h}{mv}\\ \lambda =\frac{6.626\times {10}^{-34}}{70\times 8.5}\\ \lambda =1.1\times {10}^{-36}\text{m}\end{array}$

Conclusion:

de Broglie wavelength of the bowling ball is $1.1\times {10}^{-36}\text{m}$ .

b.

To determine

To Explain: Bowling ball exhibits no observable wave behavior.

Explanation of Solution

Introduction:

de Broglie wavelength can be obtained by:

  $\lambda =\frac{h}{mv}$

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

Wave behavior of macroscopic objects like bowling ball is not visible because macroscopic objects have much larger mass than microscopic objects

The de Broglie wavelength is contrariwise related to the mass of the body. As the mass of the macroscopic objects is large, the de Broglie wavelength is so small that its wave nature is not observable.

Conclusion:

Hence, bowling ball’s mass is so large that its wave nature cannot be observed.