Chapter 27, Problem 15Q

To determine

Which one have shorter wavelength when both proton and electron travels with same speed.

Answer to Problem 15Q

Solution:

Proton will have shorter wavelength.

Explanation of Solution

De Broglie Equation Definition:

The De Broglie equation is an equation used to describe the wave properties of matter, specifically the wave nature of the electron.

De Broglie wavelength of a particle:

$\lambda =\frac{\text{h}}{\text{p}}$

$=\frac{\text{h}}{\text{mv}}$ (Particle also have $\lambda$ related to their momentum)

Where $\lambda$ is wavelength, h is plank’s constant, m is the mass of a particle (rest), v is moving velocity.

According to De Broglie above equation, the wavelength of any particulate matter is inversely proportional to it mass and varies directly with respect to its velocity. Considering the fact that the both the particles mentioned above move at the same speed, mass will be considered.

Thus mass of proton is greater (about 1800 times)than mass of electron hence mass is inversely proportional to wavelength. Which means greater mass particle have shorter wavelength and lesser mass particle have longer wavelength.