A particle moves in a closed orbit around the origin, due to a force which is directed towards the origin. The de Broglie wavelength of the particle varies cyclically between two values $λ_1$ and $λ_2$ with $λ_1>λ_2$. Which of the following statements is true?
Answer & explanation
Correct answer: option 2
The de Broglie wavelength of the particle can be varying cyclically between two values $λ_1$ and $λ_2$, if particle is moving in an elliptical orbit with origin as its one focus.
Let $v_1 , v_2$ be the speed of particle at A and B respectively and origin is at focus O. If $λ_1,λ_2$ are the de Broglie wavelengths associated with particle while moving at A and B respectively.
Then
$λ_1=\frac{h}{mv_1}$ and $λ_2=\frac{h}{mv_2}$
$∴\frac{λ_1}{λ_2}=\frac{v_2}{v_1}$
Since $λ_1>λ_2$
$∴v_2>v_1$
Thus, option (2) is true.