A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 × 10 –4 . The mass of the particle is close to

Solution

Physics sir · 4 steps

Write λ = h/mv for both, divide, and the speed ratio of 5 tells you how heavy the particle is.

1. Take the ratio. The de Broglie wavelength is λ = h/mv. Dividing the particle's wavelength by the electron's cancels h, leaving only masses and speeds.

   λₚ/λₑ = (mₑ vₑ)/(mₚ vₚ) = mₑ/(5 mₚ)

2. Solve for the mass. Rearranging gives mₚ = mₑ/(5 × 1.878 × 10⁻⁴) = (9.1 × 10⁻³¹)/(9.39 × 10⁻⁴).
3. Put in numbers. 9.1/9.39 = 0.969, so mₚ = 0.969 × 10⁻²⁷ kg = 9.69 × 10⁻²⁸ kg.
4. So. The particle's mass is close to 9.7 × 10⁻²⁸ kg, option (d).

The idea to keep. For comparing two de Broglie wavelengths, write λ = h/mv for each and divide. h cancels, and the wavelength ratio is the inverse of the momentum ratio.

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