1. Tardigrade
  2. Question
  3. Chemistry
  4. The two particles A and B have de-Broglie wavelength 1 nm and 5 nm respectively. If mass of A is four times the mass of the B, the ratio of kinetic energies of A and B would be

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Q. The two particles A and B have de-Broglie wavelength $1\, nm$ and $5\, nm$ respectively. If mass of A is four times the mass of the B, the ratio of kinetic energies of A and B would be

Structure of Atom

Solution:

$\frac{\lambda_{A}}{\lambda_{B}} = \sqrt{\frac{m_{A}E_{A}}{m_{B}E_{B}} }$
$\therefore \frac{E_{A}}{E_{B}} = \left[\frac{\lambda_{B}}{\lambda_{A}}\right]^{2} \frac{m_{B}}{m_{A}} $
$=\left(\frac{5}{1}\right)^{2}\times \frac{1}{4} = \frac{25}{4}$