Question

An electron and a proton have the same kinetic energy. Which has the greater de Broglie wavelength?

Short answer

The electron has greater de Broglie wavelength than proton.

Step-by-step solution

Describe the de Broglie wavelength

The de Broglie wavelength is given by,

$\mathit{\lambda }\mathbf{=}\frac{\mathbf{h}}{\mathbf{m}\mathbf{v}}$

Here, h is the plank’s constant, m is the mass and v is the velocity.

Find the particle which has greater de Broglie wavelength

From the de Broglie wavelength, it can be observed that the mass of the particle is inversely proportional to the wavelength.

It is known that the mass of the proton is $m_p=1.67\times {10}^{-27}\text{kg}$ and the mass of the electron is $m_e=9.11\times {10}^{-31}\text{kg}$. Clearly, the mass of the proton is more than the mass of the electron. So, the de Broglie wavelength of electron will be more than the de Broglie wavelength of proton.

Therefore, the electron has greater de Broglie wavelength than proton.