Question

Calculate the de Broglie wavelength (in nm) of a 0.700 kg tennis ball moving with a speed of 45.0 m/s (about 100 mi/h).

Answer 1

First, calculate the momentum of the tennis ball:

p = m * v
p = 0.700 kg * 45.0 m/s
p = 31.5 kg*m/s

Next, calculate the de Broglie wavelength using the formula:

λ = h / p

where h is the Planck constant (6.626 x 10^-34 J.s).

λ = 6.626 x 10^-34 J.s / 31.5 kg*m/s
λ = 2.103 x 10^-35 m

Converting this to nanometers:

λ = 2.103 x 10^-35 m * 10^9 nm/m
λ ≈ 2.103 nm

Therefore, the de Broglie wavelength of a 0.700 kg tennis ball moving with a speed of 45.0 m/s is approximately 2.103 nm.