Question

(a). What is the de Broglie wavelength of a $200\mathrm{g}$baseball with a speed of $30\mathrm{m}/\mathrm{s}$?

(b). What is the speed of a $200\mathrm{g}$baseball with a de Broglie wavelength of $0.20\mathrm{nm}$?

Short answer

(a). de Broglie wavelength of a $200g$baseball with a speed of $30m/s$is $\lambda =1.1·{10}^{-34}\mathrm{m}$.

(b). speed of a$200g$baseball$v=1.66·{10}^{-23}\frac{\mathrm{m}}{\mathrm{s}}$.

Step-by-step solution

part(a) Step 1: Given information

$200\mathrm{g}$baseball with a speed of $30\mathrm{m}/\mathrm{s}$.

part(a) step 2: Calculation

We can start the solution with expression for de-Broglie wavelength

$$\begin{gathered} \lambda =\frac{h}{mv} \\ \lambda =\frac{6.63·{10}^{-34}}{0.2·30} \\ \lambda =1.1·{10}^{-34}\mathrm{m} \end{gathered}$$

part(b) step 1: Given information

$200\mathrm{g}$baseball with a de Broglie wavelength of $0.20\mathrm{nm}$

part(b) Step 2: Calculation

with same expression we can find speed of a $200\mathrm{g}$baseball:

$$\begin{gathered} v=\frac{h}{m\lambda } \\ v=\frac{6.63·{10}^{-34}}{0.2·0.2·{10}^{-9}} \\ v=1.66·{10}^{-23}\frac{m}{s} \end{gathered}$$