AP EAMCET · PHYSICS · Atomic Physics

The difference between the radii of $n^{th}$ and $(n + 1)^{t h}$ orbits of hydrogen atom is equal to the radius of $(n - 1)^{th}$ orbit of hydrogen. The angular momentum of the electron in the $n^{th}$ orbit is $______$ ( $h$ is Planck's constant)

A $\frac{h}{π}$
B $\frac{2 h}{π}$
C $\frac{3 h}{π}$
D $\frac{4 h}{π}$

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Answer & Solution

Correct Answer

(B) $\frac{2 h}{π}$

Step-by-step Solution

Detailed explanation

The radius of the hydrogen atom, rn=r0n2 ⇒rn+1=r0n+12, rn=r0n2 & rn-1=r0n-12⇒rn+1-rn=rn-1⇒r0n+12-r0n2=r0n-12⇒n+12-n2=n-12⇒2n+1=n2+1-2n⇒4n=n2⇒n=4 now Recall the Bohr's second postulate,…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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The difference between the radii of nth and (n+1)th orbits of hydrogen atom is equal to the radius of (n-1)th orbit of hydrogen. The angular momentum of the electron in the nth orbit is______(h is Planck's constant)

Step-by-step Solution

The difference between the radii of $n^{th}$ and $(n + 1)^{t h}$ orbits of hydrogen atom is equal to the radius of $(n - 1)^{th}$ orbit of hydrogen. The angular momentum of the electron in the $n^{th}$ orbit is $______$ ( $h$ is Planck's constant)