We appreciate your visit to Calculate the wavelengths of the first three lines in the Lyman series those for which tex n i 2 3 text and 4 tex Enter. This page offers clear insights and highlights the essential aspects of the topic. Our goal is to provide a helpful and engaging learning experience. Explore the content and find the answers you need!
Answer :
Final answer:
The wavelengths of the first three lines in the Lyman series, for transitions to the n = 1 orbit with initial states n_i = 2, 3, and 4, are 121.6 nm, 102.6 nm, and 97.3 nm respectively. These calculations use the Rydberg equation for hydrogen's spectral lines.
Explanation:
To calculate the wavelengths of the first three lines in the Lyman series, we use the Rydberg equation:
\[\frac{1}{\lambda} = R \left( \frac{1}{1^2} - \frac{1}{n_i^2} \right)\]
Where \(\lambda\) is the wavelength, \(R\) is the Rydberg constant (1.097 x 10^7 m^-1), \(n_i\) is the initial energy level, and we are considering transitions to the n = 1 orbit (ground state).
For the first line (n_i = 2):
\[\frac{1}{\lambda} = 1.097 \times 10^7 \left(1 - \frac{1}{2^2}\right)\]
\[\lambda = 121.6 \text{ nm}\]
For the second line (n_i = 3):
\[\frac{1}{\lambda} = 1.097 \times 10^7 \left(1 - \frac{1}{3^2}\right)\]
\[\lambda = 102.6 \text{ nm}\]
For the third line (n_i = 4):
\[\frac{1}{\lambda} = 1.097 \times 10^7 \left(1 - \frac{1}{4^2}\right)\]
\[\lambda = 97.3 \text{ nm}\]
Thus, the wavelengths of the first three lines in the Lyman series in decreasing order are: 121.6 nm, 102.6 nm, and 97.3 nm. Therefore, the correct answer is b) 121.6nm, 102.6nm, 97.3nm.
Thanks for taking the time to read Calculate the wavelengths of the first three lines in the Lyman series those for which tex n i 2 3 text and 4 tex Enter. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!
- Why do Businesses Exist Why does Starbucks Exist What Service does Starbucks Provide Really what is their product.
- The pattern of numbers below is an arithmetic sequence tex 14 24 34 44 54 ldots tex Which statement describes the recursive function used to..
- Morgan felt the need to streamline Edison Electric What changes did Morgan make.
Rewritten by : Barada
