Calculate the de Broglie wavelength of (a) a tennis ball of mass 57 g traveling 25 m/s (about 56 mph) and (b) an electron with kinetic energy 50 eV.

Strategy The calculation for both of these wavelengths is a straightforward application of Equation (5.2).

$\lambda=\frac{h}{p}$ (5.2)

Question

Calculate the de Broglie wavelength of (a) a tennis ball of mass 57 g traveling 25 m/s (about 56 mph) and (b) an electron with kinetic energy 50 eV.

Strategy The calculation for both of these wavelengths is a straightforward application of Equation (5.2).

[latex]\lambda=\frac{h}{p}[/latex] (5.2)

Accepted Answer

(a) For the tennis ball, m = 0.057 kg, so

[latex]\lambda=\frac{h}{p}=\frac{6.63 imes 10^{-34} J \cdot s }{(0.057 kg )(25 m / s )}=4.7 imes 10^{-34} m[/latex]

(b) For the electron, it is more convenient to use eV units, so we rewrite the wavelength λ as

[latex]\lambda=\frac{h}{p}=\frac{h}{\sqrt{2 m K}}=\frac{h c}{\sqrt{2\left(m c^{2} ight) K}}[/latex]

[latex]\lambda=\frac{1240 eV \cdot nm }{\sqrt{(2)\left(0.511 imes 10^{6} eV ight)(50 eV )}}=0.17 nm[/latex]

Note that because the kinetic energy of the electron is so small, we have used a nonrelativistic calculation. Calculations in modern physics are normally done using eV units, both because it is easier and also because eV values are more appropriate for atoms and nuclei (MeV, GeV) than are joules. The values of hc and some masses can be found inside the front cover.

Question 5.2: Calculate the de Broglie wavelength of (a) a tennis ball of ...

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