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In a sample of H-atoms electrons are de-...

In a sample of H-atoms electrons are de-exicited from `4^(th)` excited state to ground state. Which is/are correct statement ?

A

(a) No line observed in P-fund series.

B

(b) Total ten lines observed in spectrum.

C

(c) `4` line in UV-region and `3` line in visible region observed.

D

(d) One line observed in Brackett series.

Text Solution

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The correct Answer is:
To solve the question regarding the de-excitation of electrons in hydrogen atoms from the fourth excited state to the ground state, we will follow these steps: ### Step-by-Step Solution: 1. **Identify the Energy Levels**: - The ground state of hydrogen corresponds to \( n = 1 \). - The first excited state corresponds to \( n = 2 \). - The second excited state corresponds to \( n = 3 \). - The third excited state corresponds to \( n = 4 \). - The fourth excited state corresponds to \( n = 5 \). 2. **Determine the Transition**: - The transition described in the question is from \( n = 5 \) (fourth excited state) to \( n = 1 \) (ground state). 3. **Identify the Series**: - Transitions to \( n = 1 \) correspond to the Lyman series, which is in the ultraviolet (UV) region. 4. **Calculate the Number of Spectral Lines**: - The number of spectral lines produced during a transition from \( n = 5 \) to \( n = 1 \) can be calculated using the formula: \[ \text{Number of lines} = \frac{n(n-1)}{2} \] where \( n \) is the upper energy level (in this case, \( n = 5 \)). - Substituting the values: \[ \text{Number of lines} = \frac{5 \times 4}{2} = 10 \] 5. **Identify the Regions of the Spectrum**: - The Lyman series (from \( n = 2 \) to \( n = 1 \)) consists of 4 lines in the UV region. - The Balmer series (from \( n = 3 \) to \( n = 2 \)) consists of 3 lines in the visible region. - The Paschen series (from \( n = 4 \) to \( n = 3 \)) consists of 4 lines in the infrared region. - The Brackett series (from \( n = 5 \) to \( n = 4 \)) consists of 1 line in the infrared region. - The Pfund series (from \( n = 6 \) to \( n = 5 \)) consists of lines in the infrared region. 6. **Evaluate the Statements**: - **Statement 1**: No line is observed in the Pfund series. (Correct) - **Statement 2**: A total of 10 lines are observed in the spectrum. (Correct) - **Statement 3**: 4 lines lie in the UV region and 3 lines lie in the visible region. (Correct) - **Statement 4**: 1 line is observed in the Brackett series. (Correct) ### Conclusion: All four statements are correct.
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