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PhysicsModern PhysicsAtomic structureEasy2 minPYQ_2020

PhysicsEasysingle choice

Let $A_{n}$ be the area enclosed by the $n^{t h}$ orbit in a hydrogen atom. The graph of $l n (\frac{A_{n}}{A_{1}})$ against $\ln (n)$

Options:

Answer:

Solution:

We know that the radius of the $n^{th}$ stationary orbit is

$R_{n} = R_{0} n^{2}$
$∴$ $A_{n} = 4 π R_{0}^{2} \cdot n^{4}$
and, $A_{1} = 4 π R_{0}^{2}$
$∴$ $\frac{A_{n}}{A_{1}} = n^{4}$
$\Rightarrow$ $l n (\frac{A_{n}}{A_{1}}) = 4 l n n$
The graph is a straight line of slope $4$ and passes through the origin.

Stream:NTA_ABHYAS_NEETSubject:PhysicsTopic:Modern PhysicsSubtopic:Atomic structure

⏱ 2mℹ️ Source: PYQ_2020

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