Two subatomic particles 1 and 2, with the same kinetic energies have their de- Broglie wavelengths as ₁ & ₂ and masses as 3 m and 6 m respectively. Determine the ratio ₁: ₂ .

Step-by-step solution

The de-Broglie wavelength is given by the relation = h p , where p is the momentum of the particle. The relationship between kinetic energy K and momentum p is K = p^2 2m , which implies p = 2mK . Substituting this into the wavelength formula, we get = h 2mK . Given that both particles have the same kinetic energy K , the wavelength is inversely proportional to the square root of the mass, 1 m . Therefore, the ratio of the wavelengths is ₁ ₂ = m₂ m₁ . Given m₁ = 3m and m₂ = 6m , we have ₁ ₂ = 6m 3m = 2 . Thus, the