Question 7.PS.5: Tennis Balls and Electrons At Wimbledon, tennis serves routi......

The wavelength of the electron is much longer than that of the tennis ball: electron = 0.15  nm; tennis ball = 2.09 × 10^{-25}   nm.

Strategy and Explanation We can substitute the mass and velocity into the de Broglie wave equation to calculate the corresponding wavelength. Planck’s constant, b, is

6.626 × 10^{-34}  J⋅s, and 1  J = \frac{1  kg⋅m^2}{s^2} so that b =  6.626 × 10^{-34}  kg⋅m^2  s^{-1}.

For the electron:

λ = \frac{6.626 × 10^{-34}  kg⋅m^2  s^{-1}}{(9.11 × 10^{-31}  kg)(5.0 × 10^6  m/s)} = 1.5 × 10^{-10}  m × \frac{1  nm}{10^{-9}  m} = 0.15  nm

For the tennis ball:

λ = \frac{6.626 × 10^{-34}  kg⋅m^2  s^{-1}}{(0.0567  kg)(56.0  m/s)} = 2.09 × 10^{-34}  m × \frac{1  nm}{10^{-9}  m} = 2.09 × 10^{-25}  nm

The wavelength of the electron is in the X-ray region of the electromagnetic spectrum (Figure 7.1, ← p. 222). The wavelength of the tennis ball is far too short to observe.