Question

Out of electron and proton which one will have, a higher velocity to produce matter waves of the same wavelength? Explain it

Answer 1

Calculating velocity of particles using de-Broglie's relation

According to de-Broglie’s relation:

$\lambda =\frac{h}{mv}$

where, $\lambda$ is wavelength, ℎ is Planck’s constant 𝑚 is mass and 𝑣 is velocity.

$\to \lambda \alpha \frac{1}{mv}$

From this, we observed that wavelength is inversely proportional to mass and velocity.


For the same wavelength, object with large mass, will have smaller velocity and object with smaller mass will have larger velocity, in order to keep the value of wavelength constant.


Among proton and electron, the mass of electron is less than the mass of proton.

Mass of electron$\left(m_e\right)=9.1\times {10}^{-31}kg$

Mass of proton$\left(m_p\right)=1.6726\times {10}^{-27}kg$

Therefore, electron will have higher velocity as compared to the velocity of proton.