Question

Using de Broglie's equation, λ = h/mv which would have a larger wavelength, a slow-moving proton or a fast-moving golf ball? Explain your answer.

Answer 1

Answer: Proton will have larger wavelength

Explanation:

$\lambda =\frac{h}{mv}$  (de-Broglie's equation)

$\lambda =\text{wavelenght of the particle}$

h= Planck constant

m= mass of the particle

v= velocity of the particle

As we can see from the de-Broglie's equation , that wavelength is inversely proportional to the product of mass into velocity of the object.

The wavelength of proton will be higher than that fast moving golf ball because mass of proton $(1.67 \times 10^{-24}g)$ is very small than that of the golf ball (45.93 g). Proton is moving  at slow velocity and the golf ball is moving with fast velocity by which value of product of mass into velocity of proton will be lower than the value of product of mass into velocity of the golf ball which will result in larger value of wavelength of the proton.