Modern Physics 1 Question 32
29. The allowed energy for the particle for a particular value of $n$ is proportional to
(a) $a^{-2}$
(b) $a^{-3 / 2}$
(c) $a^{-1}$
(d) $a^{2}$
(2009)
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Solution:
$$ \begin{aligned} & \quad a=\frac{n \lambda}{2} \\ & \therefore=\frac{2 a}{n}=\frac{h}{p}=\frac{h}{\sqrt{2 E m}} \\ & \text { or } \quad \sqrt{E} \propto \frac{1}{a} \Rightarrow \quad \therefore E \propto \frac{1}{a^{2}} \end{aligned} $$
