The ratio of the shortest wavelengths of two spectral series of hydrogen spectrum is found to be 9 (Nine). The spectral series are -

This question was previously asked in
HPSC Assistant Professor 2018 Chemistry (Official Paper)
View all HPSC Assistant Professor Papers >
  1. Balmer and Brackett
  2. Lyman and Paschen
  3. Paschen and Pfund 
  4. Brackett and Pfund

Answer (Detailed Solution Below)

Option 2 : Lyman and Paschen
Free
HPSC Asst Prof. Commerce Subject Test 1
1.2 K Users
20 Questions 20 Marks 25 Mins

Detailed Solution

Download Solution PDF

CONCEPT:

Spectral Series in Hydrogen Spectrum

  • The wavelengths of the spectral lines in the hydrogen spectrum can be determined using the Rydberg formula:
    • \(\frac{1}{\lambda} = R \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} \right)\)
  • Here, R is the Rydberg constant (\( R \approx 1.097 \times 10^7 \, \text{m}^{-1}\) ), n1 is the lower energy level, and n2 is the higher energy level ( n2 > n1 ).
  • For Lyman series, n1 = 1 ; for Balmer series, n1 = 2 ; for Paschen series, n1 = 3 ; for Brackett series, n1 = 4 ; and for Pfund series, n1 = 5 .
  • The shortest wavelength in any series corresponds to the transition where n_2 approaches infinity ( n2 to \(\infty\)  ).

EXPLANATION:

  • For Lyman series ( n1 = 1 ):
    • \(\frac{1}{\lambda_{\text{Lyman}}} = R \left( \frac{1}{1^2} - \frac{1}{\infty^2} \right) = R \)
    • Therefore, \(\lambda_{\text{Lyman}} = \frac{1}{R} .\)
  • For Paschen series ( n1 = 3 ):
    • \(\frac{1}{\lambda_{\text{Paschen}}} = R \left( \frac{1}{3^2} - \frac{1}{\infty^2} \right) = \frac{R}{9} \)
    • Therefore, \(\lambda_{\text{Paschen}} = \frac{9}{R}\) .
  • The ratio of the shortest wavelengths is:
    • \(\frac{\lambda_{\text{Paschen}}}{\lambda_{\text{Lyman}}} = \frac{\frac{9}{R}}{\frac{1}{R}} = 9\)

The correct option is Lyman and Paschen

Latest HPSC Assistant Professor Updates

Last updated on May 30, 2025

-> The HPSC Assistant Professor Result has been announced for the screening test of Assistant Professor Botany and Zoology posts.

-> The HPSC Assistant Professor Subject Knowledge Test is scheduled on various days between 25th April to 31st August 2025, and the Screening Test will be conducted between 27th April to 29th June 2025.

-> The Skill Test (Fine Arts & Music) was conducted from 4th to 12th April 2025.

-> HPSC Assistant Professor Notification (2024) was released for 2424 vacancies.

-> The commission has decided to conduct the Exams through a Screening Test followed by a Subject Knowledge Test (87.5% weightage) and Interview (12.5 % weightage).

-> Candidates who have completed their Post Graduation are eligible to apply for the post.

-> After getting a successful selection, the candidates will receive a decent salary range between Rs. 57,700 - Rs. 1,82,400.

Get Free Access Now
Hot Links: teen patti joy apk teen patti sweet teen patti gold new version 2024