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What are the values of n(1) and n(2) res...

What are the values of `n_(1)` and `n_(2)` respectively for `H_(B)` line in the Lyman series of hydrogen atom spectrum?

A

3 and 5

B

2 and 3

C

1 and 3

D

2 and 4

Text Solution

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The correct Answer is:
To determine the values of \( n_1 \) and \( n_2 \) for the \( H_\beta \) line in the Lyman series of the hydrogen atom spectrum, we can follow these steps: ### Step 1: Understand the Lyman Series The Lyman series consists of spectral lines resulting from electronic transitions in a hydrogen atom where the electron falls to the first energy level (ground state). In this series, transitions occur from higher energy levels to \( n_1 = 1 \). ### Step 2: Identify the \( H_\beta \) Line The \( H_\beta \) line refers to the second line in the Lyman series. The nomenclature \( H_\beta \) indicates that it is the second line (beta) of the series. ### Step 3: Determine \( n_1 \) Since the Lyman series always ends at \( n_1 = 1 \) (the ground state), we can conclude: \[ n_1 = 1 \] ### Step 4: Determine \( n_2 \) For the \( H_\beta \) line, we need to identify the higher energy level from which the electron transitions down to \( n_1 \). The second line in the Lyman series corresponds to a transition from \( n_2 = 3 \) to \( n_1 = 1 \). Thus, we have: \[ n_2 = 3 \] ### Conclusion The values of \( n_1 \) and \( n_2 \) for the \( H_\beta \) line in the Lyman series are: \[ n_1 = 1, \quad n_2 = 3 \] ### Final Answer The values of \( n_1 \) and \( n_2 \) respectively for the \( H_\beta \) line in the Lyman series of hydrogen atom spectrum are \( n_1 = 1 \) and \( n_2 = 3 \). ---
To determine the values of \( n_1 \) and \( n_2 \) for the \( H_\beta \) line in the Lyman series of the hydrogen atom spectrum, we can follow these steps: ### Step 1: Understand the Lyman Series The Lyman series consists of spectral lines resulting from electronic transitions in a hydrogen atom where the electron falls to the first energy level (ground state). In this series, transitions occur from higher energy levels to \( n_1 = 1 \). ### Step 2: Identify the \( H_\beta \) Line The \( H_\beta \) line refers to the second line in the Lyman series. The nomenclature \( H_\beta \) indicates that it is the second line (beta) of the series. ...
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