Question

What is the de Broglie wavelength (in meters) of a 58.1 g tennis ball when served at a velocity of 44.5 meters per second?

a. 5.36×10−345.36×10 −34
b. 2.48×10−342.48×10 −34
c. 1.25×10−341.25×10 −34
d. 9.72×10−349.72×10 −34

Answer 1

The de Broglie wavelength for a tennis ball of mass 58.1 g served at a velocity of 44.5 m/s is approximately 2.56×10⁻³⁴ meters, which does not match any of the provided options.

Step-by-step explanation:

To calculate the de Broglie wavelength of an object, we use the formula λ = h / (mv), where λ is the wavelength, h is the Planck's constant (6.626×10⁻³⁴ J·s), m is the mass of the object in kilograms, and v is the velocity in meters per second. For a 58.1 g tennis ball, which is 0.0581 kg, served at a velocity of 44.5 m/s, we can calculate the wavelength as follows:

λ = h / (mv) = 6.626×10⁻³⁴ J·s / (0.0581 kg × 44.5 m/s) = 6.626×10⁻³⁴ J·s / (2.58845 kg·m/s) ≈ 2.56×10⁻³⁴ meters

None of the options listed match this calculated result, which indicates a possible error in the question or the options provided.