Chapter 6, Problem 6.1P

To determine

De Broglie wavelength of rain drops.

Answer to Problem 6.1P

  $\lambda =6.63\times {10}^{-26}\text{m}$

Explanation of Solution

Given:

Mass of the raindrop, $m=1\text{mg =}1\times {10}^{-6}\text{kg}$

Speed of the raindrop, $v=1\text{cm}/\text{s = }1\times {10}^{-2}\text{m}/\text{s}$

Formula used:

Momentum, $p=mv$

Calculation:

Momentum, $p=mv$

  $=\left(1\text{mg}\right)\left(1\frac{\text{cm}}{\text{s}}\right)$

  $=\left(1\times {10}^{-6}\text{kg}\right)\left(1\times {10}^{-2}\text{m}/\text{s}\right)$

  $=1\times {10}^{-8}\text{kg}.\text{m}/\text{s}$

De Broglie wavelength associate with this raindrop, $\lambda =\frac{h}{p}$

  $=\frac{6.63\times {10}^{-34}\text{J}.\text{s}}{1\times {10}^{-8}\text{kg}.\text{m}/\text{s}}$

  $=6.63\times {10}^{-26}\text{m}$

Conclusion:

  $\lambda =6.63\times {10}^{-26}\text{m}$

This wavelength is very small and cannot be detected.