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AP EAMCET · Chemistry · Structure of Atom

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

  1. A 3 : 2
  2. B \(\sqrt{3}: \sqrt{2}\)
  3. C \(\sqrt{2}: \sqrt{3}\)
  4. D 2 : 3
Verified Solution

Answer & Solution

Correct Answer

(B) \(\sqrt{3}: \sqrt{2}\)

Step-by-step Solution

Detailed explanation

de-Broglie's wavelength is given by the equation \(\lambda=\frac{h}{p}\) To find the ratio of the wavelength, we need the ratio of \(p\), where \(p=m v\) \[ p=m v=\sqrt{m^2 v^2}=\sqrt{2 m\left(\frac{1}{2} m v^2\right)}=\sqrt{2 m K} \] where, \(m\) is mass and \(K\) is kinetic…