When the electron of 5th orbit jumps into the first hour with the number of spectral lines produced in hydrogen spectrum is?

India's Super Teachers for all govt. exams Under One Roof

Enroll For Free Now

Content: 

As per the Bohr model of an atom, electron revolves around the nucleus in fixed orbits. While in these orbits it does not radiate energy. It radiates energy only when it jumps from one allowed energy level to another. Each jump or transition gives a unique spectral line. Since the number of allowed transitions is fixed so the number of spectral lines is also fixed. 

The Number of possible spectral lines is a combination of n possible transitions between two energy levels (initial and final) i.e. 

\(^nC_2 = \dfrac{n!}{2!(n-2)!}=\dfrac{n^2-n}{2}\)

        = \(\dfrac{n(n-1)}{2}\)

The wavelength can be calculated using the mathematical formula

 \(\dfrac{1}{\lambda}=R \left(\dfrac{1}{n_f^2} - \dfrac{1}{n_i^2}\right)\) , where ni and nf are initial and final shell respectively

Explanation:

Given: n = 5

So total number of spectral lines is given by 

\(\dfrac{n(n-1)}{2}=10\)

So, there will be 10 spectral lines in total.

Option(4) is the correct answer. 

For low levels, you can actually draw all the possible transitions and count them. But this is difficult when n is large. 

For transitions from n=1 to n=5 (or from n=5 to n=1), the following transitions can take place: 

1. 5→ 4
2. 5→ 3
3. 5→ 2
4. 5 → 1
5. 4 → 3
6. 4→ 2
7. 4→ 1
8. 3 → 2
9. 3→ 1
10. 2 → 1 

India’s #1 Learning Platform

Start Complete Exam Preparation

Daily Live MasterClasses

Practice Question Bank

Mock Tests & Quizzes

Get Started for Free Download App

Trusted by 3.3 Crore+ Students