A particle is travelling 4 time as fast as an electron. Assuming the ratio of de-Broglie wavelength of a particle to that of electron is 2 : 1, the mass of the particle is :

Solution

Physics sir · 4 steps

Write λ = h/mv for both and take the ratio. h cancels, and the mass ratio falls out.

1. de Broglie relation. For any moving particle, λ = h/mv. Write it once for the particle and once for the electron, then divide.

   λₚ/λₑ = (mₑ vₑ)/(mₚ vₚ)

2. Put in numbers. The particle moves 4 times as fast, so vₚ = 4vₑ. The wavelength ratio is λₚ/λₑ = 2. This gives 2 = (mₑ vₑ)/(mₚ × 4vₑ) = mₑ/4mₚ.
3. Solve for mass. Rearranging, 8mₚ = mₑ, so mₚ = mₑ/8.
4. So. The particle's mass is 1/8 times the mass of the electron, which is option (d).

The idea to keep. Wavelength goes as 1/(mv). A particle that is faster and also has a longer wavelength must be much lighter, so check the direction of your answer before choosing.

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