A particle of mass m is dropped on an elastic ground from a height H . The gravi | TestHub

Passage / Comprehension

Bohr and Sommerfeld postulated the periodic motion of a particle moving in a conservative force field. They stated that the momentum $p$ and displacement $s$ are related by the following quantization rule:

$\oint p \cdot d s = nh$

Where $\oint$ denotes the integral over a single periodic closed path. For example, for an electron moving in a circular path in a hydrogen atom:

$\oint p d s = nh$

Since $p$ is constant in a circular path, $m v \times 2 π r = nh$ , which is Bohr's quantization principle for the Bohr atom. Now, we apply this condition to other periodic motions.

A particle of mass $m$ is dropped on an elastic ground from a height $H$ . The gravitational field is constant and has a magnitude g. This postulate yields that if in ground state $H = H_{0}$ , in first excited state, $H = 2^{n} H_{0}$ . Find $n$ + 0.34 ?

Answer:

1.00

Solution:

$mv (2 π r) = nh$ with $mv = B_{0} qr$

$\Rightarrow r \propto n^{1/2} \Rightarrow \frac{r _{5}}{r _{3}} = \frac{5}{3} \approx 1.291$

Physics - Modern Physics Question with Solution | TestHub

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