The wavelength of an electron and a neutron will become equal when the velocity of the electron is x times the velocity of neutron. The value of x is ____________. (Nearest Integer)
(Mass of electron is 9.1 × 10⁻³¹ kg and mass of neutron is 1.6 × 10⁻²⁷ kg )

Solution

Chemistry ma’am · 3 steps

Same wavelength means same momentum, so the lighter electron must move faster by the mass ratio.

1. Equal wavelengths. The de Broglie wavelength is λ = h/mv. If the two wavelengths are equal, then mv must be the same for the electron and the neutron.

   mₑ vₑ = mₙ vₙ ⇒ x = vₑ/vₙ = mₙ/mₑ

2. Put in numbers. x = (1.6 × 10⁻²⁷)/(9.1 × 10⁻³¹) = 0.17582 × 10⁴ = 1758.2.
3. So. The electron must move about 1758 times faster than the neutron, so x = 1758.

The idea to keep. For particles with equal de Broglie wavelengths, momentum is equal. Velocity is then inversely proportional to mass, so the lighter particle moves faster.

Answer from the NTA final answer key. Solution by PrepWiser.