Question: Q. 1. A particle is dropped from a height 1. The deBroglie wavelength of the particle as a function of height is proportional to (a) $H$. (c) $H^{0}$.
[NCERT Exemplar]
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Solution:
Ans. Correct option : (d)
Explanation: Velocity $v$, of freely falling body after falling from a height $H$, will be :
$$ H=v=\sqrt{2 g H} $$
We know that de-Broglie wavelength $\lambda=\frac{h}{p}$
$$ \lambda=\frac{h}{m v}=\frac{h}{m \sqrt{2 g H}} $$
$h, m$, and $g$ are constant
$\therefore \frac{h}{m \sqrt{2 g}}$ is constant $\Rightarrow \lambda \propto \frac{1}{\sqrt{H}} \Rightarrow \lambda \propto H^{-1 / 2}$
