સ્નાયુઓના દુખાવાના ઉષ્મા ઉપચારમાં આશરે 900 nm તરંગલંબાઈના વિકિરણનો સમાવેશ થાય છે. H પરમાણુની કઈ વર્ણપટ રેખા આ માટે યોગ્ય છે?
આપેલ છે: રિડબર્ગ અચળાંક \(\mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1}, \mathrm{~h}=6.6 \times 10^{-34} \mathrm{~J} \mathrm{~s}, \mathrm{c}=3 \times 10^8 \mathrm{~m} / \mathrm{s}\)

A બામર શ્રેણી, \(\infty \rightarrow 2\)
B લાઇમન શ્રેણી, \(\infty \rightarrow 1\)
C પાશ્ચન શ્રેણી, \(\infty \rightarrow 3\)
D પાશ્ચન શ્રેણી, \(5 \rightarrow 3\)

Verified Solution

Answer & Solution

Correct Answer

(C) પાશ્ચન શ્રેણી, \(\infty \rightarrow 3\)

Step-by-step Solution

Detailed explanation

\begin{aligned} & \lambda=900 \mathrm{~nm} \quad \text { H-atom }(\mathrm{Z}=1) \\ & =9 \times 10^{-5} \mathrm{~cm} \\ & \mathrm{R}_{\mathrm{H}}=10^5 \mathrm{~cm}^{-1} \\ & \text { Ryderg eq. }=\frac{1}{\lambda}=\mathrm{R}_{\mathrm{H}} \mathrm{Z}^2…

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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