Final answer:
The de Broglie wavelength for an electron moving at 30% the speed of light is approximately 0.00801 nm. For a 55 g tennis ball served at 57 m/s, the wavelength is roughly 0.0000000000217 nm.
Step-by-step explanation:
The de Broglie wavelength can be calculated using the formula λ = h / (mv), where λ is the wavelength, h is Planck's constant (6.626 × 10-34 m·kg/s), m is the mass of the particle, and v is its velocity.
Electron:
The velocity of the electron is 30% of the speed of light, which is approximately 3 × 108 m/s. Thus, v = 0.3 × 3 × 108 m/s = 9 × 107 m/s. The mass of an electron is 9.109 × 10-31 kg. Using the de Broglie formula:
λ = 6.626 × 10-34 m·kg/s / (9.109 × 10-31 kg × 9 × 107 m/s) ≈ 8.01 × 10-12 m or 0.00801 nm.
Tennis Ball:
The mass of the tennis ball is 55 g, which is equal to 0.055 kg. Using the given velocity, v = 57 m/s, the de Broglie wavelength is:
λ = 6.626 × 10-34 m·kg/s / (0.055 kg × 57 m/s) ≈ 2.17 × 10-34 m or 0.0000000000217 nm.