Verified Solution • 2025–26 Session moderate

QPages 384-386: Q7: HC Verma: Concepts of Physics - Volume 2 Bohr's Model and Physics of the Atom Pages 384-386: Q7 Solution: A hydrogen atom emits ultraviolet radiation of wavelength 102.5 …

⚠️ Common Exam Traps & Conceptual Pitfalls

Students often fail to deduce that ultraviolet emission in hydrogen corresponds exclusively to the Lyman series, where the final energy level is $n_f = 1$. If the final state is not correctly identified as the ground state, the Rydberg equation cannot be simplified to solve for the initial quantum number $n_i$.

A hydrogen atom emits ultraviolet radiation of wavelength 102.5 nm. What are the quantum numbers of the states involved in the transition?

Step-by-Step Verified Solution

**Answer:** The quantum numbers are n_ = 1 and n_ = 3. **Step-by-Step Explanation:** The wavelength 102.5 nm lies in the ultraviolet region, so it belongs to the Lyman series (n_ = 1). Using Rydberg's formula: 1λ=R(1−1n22)\frac{1}{\lambda} = R\left(1 - \frac{1}{n_2^2}\right). 1/(102.5×10−9)=1.097×107(1−1/n22)1/(102.5 \times 10^{-9}) = 1.097 \times 10^7 (1 - 1/n_2^2). 9.76×106=1.097×107(1−1/n22)9.76 \times 10^6 = 1.097 \times 10^7 (1 - 1/n_2^2). 1−1/n22=0.889⇒1/n22=0.111⇒n22=9⇒n2=31 - 1/n_2^2 = 0.889 \Rightarrow 1/n_2^2 = 0.111 \Rightarrow n_2^2 = 9 \Rightarrow n_2 = 3. So the transition is from n = 3 to n = 1 [citation:3][citation:11].

All Questions in this Chapter

QPage 383: Q1 QPage 383: Q2 QPage 383: Q3 QPage 383: Q4 QPage 383: Q5 QPage 383: Q6 QPage 383: Q7 QPage 383: Q8 QPage 383: Q9 QPage 383: Q10 QPage 383: Q11 QPage 383: Q12 QPage 383: Q13 QPages 382-383: Q1 QPages 382-383: Q2 QPages 382-383: Q3 QPages 382-383: Q4 QPages 382-383: Q5 QPages 382-383: Q6 QPages 382-383: Q7 QPages 382-383: Q8 QPages 382-383: Q9 QPages 382-383: Q10 QPages 383-384: Q1 QPages 383-384: Q2 QPages 383-384: Q3 QPages 383-384: Q4 QPages 383-384: Q5 QPages 383-384: Q6 QPages 384-386: Q1 QPages 384-386: Q2 QPages 384-386: Q3 QPages 384-386: Q4 QPages 384-386: Q5 QPages 384-386: Q6 QPages 384-386: Q7 QPages 384-386: Q8 QPages 384-386: Q9 QPages 384-386: Q10 QPages 384-386: Q11 QPages 384-386: Q12 QPages 384-386: Q13 QPages 384-386: Q14 QPages 384-386: Q15 QPages 384-386: Q16 QPages 384-386: Q17 QPages 384-386: Q18 QPages 384-386: Q19 QPages 384-386: Q20 QPages 384-386: Q21 QPages 384-386: Q22 QPages 384-386: Q23 QPages 384-386: Q24 QPages 384-386: Q25 QPages 384-386: Q26 QPages 384-386: Q27 QPages 384-386: Q28 QPages 384-386: Q29 QPages 384-386: Q30 QPages 384-386: Q31 QPages 384-386: Q32 QPages 384-386: Q33 QPages 384-386: Q34 QPages 384-386: Q35 QPages 384-386: Q36 QPages 384-386: Q37 QPages 384-386: Q38 QPages 384-386: Q39 QPages 384-386: Q40 QPages 384-386: Q41 QPages 384-386: Q42 QPages 384-386: Q43 QPages 384-386: Q44 QPages 384-386: Q45 QPages 384-386: Q46

Related Learning Resources & Exam Preparation

Chapter Practice Bank
Practice all topic-wise questions from Bohr's Model and Physics of the Atom
Reference Textbook Solutions
Explore complete chapter exercises for HC Verma: Concepts of Physics - Volume 2
Competitive PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring