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.