Answer
a) 2.426 x 10^-11 m
b) λ ≈ 3.43 x 10^-34 m
Work Step by Step
To calculate the de Broglie wavelength, we use the formula:
λ = h / (m * u)
where λ is the de Broglie wavelength, h is Planck's constant (6.626 x 10^-34 J/s), m is the mass of the object, and u is the velocity of the object.
a. For an electron with a velocity of 10% of the speed of light:
m = 9.12 x 10^-31 kg (mass of electron)
u = 0.1 * 3 x 10^8 m/s (10% of the speed of light)
λ = (6.626 x 10^-34) / (9.12 x 10^-31 * 3 x 10^7)
λ ≈ 2.426 x 10^-11 m
b. For a tennis ball (55 g) served at 35 m/s:
m = 0.055 kg (convert 55 g to kg)
u = 35 m/s
λ = (6.626 x 10^-34) / (0.055 * 35)
λ ≈ 3.43 x 10^-34 m
