The ratio of de-Broglie wavelengths of two particles having mass ratio 1: 3 and kinetic energy ratio 2: 1 is

Step-by-step solution

de-Broglie's wavelength is given by the equation = h p To find the ratio of the wavelength, we need the ratio of p , where p=m v p=m v= m^2 v^2 = 2 m ( 1 2 m v^2 ) = 2 m K where, m is mass and K is kinetic energy. Hence, the ratio of the wavelength is aligned ₁ ₂ & = (h / p₁ ) (h / p₂ ) = p₂ p₁ & = 2 m₂ K₂ 2 m₁ K₁ = ( m₂ m₁ ) ( K₂ K₁ ) & = 3 ( 1 2 ) = 3 2 = 3 : 2 aligned