Question

When two particles of masses m and 2m have equal kinetic energies. Find the ratio of their de Broglie wavelengths.

• A. 1:1
• B. 1:$\sqrt{2}$
• C. 1:2
• D. $\sqrt{2}$:1

Answer 1

The correct option is D $\sqrt{2}$:1

According to de Broglie the wavelength of a particle of mass m moving with velocity v is given by
$\lambda =\frac{h}{mv}=\frac{h}{\sqrt{2mE}}$
where, h= Planck's constant
v= velocity of particle
E= Kinetic energy of particle

As Kinetic energies are same for same for both m and 2m, the de Broglie wavelengths will be in the ratio

$\frac{{\left(\lambda \right)}_m}{{\left(\lambda \right)}_{2m}}=\frac{\frac{h}{\sqrt{2mE}}}{\frac{h}{\sqrt{2\left(2m\right)E}}}=\frac{\sqrt{2}}{1}$