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Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be :
- a)2
- b)3
- c)5
- d)6
Correct answer is option 'D'. Can you explain this answer?
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Hydrogen atom is excited from ground state to another state with princ...
The possible number of the spectral lines is given
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Hydrogen atom is excited from ground state to another state with princ...
Understanding Excited States of Hydrogen
When a hydrogen atom is excited to a higher energy level, it can emit light as it transitions back to lower energy levels. The principal quantum number (n) indicates the energy level; in this case, n = 4.
Calculating the Number of Spectral Lines
To determine the number of spectral lines emitted when an electron falls from level n = 4 to lower levels, we can use the following steps:
- Allowed Transitions: An electron can transition from n = 4 to n = 1, n = 2, and n = 3. Each transition emits a spectral line.
- Possible Transitions: The transitions from n = 4 can be summarized as follows:
- From n = 4 to n = 3
- From n = 4 to n = 2
- From n = 4 to n = 1
- From n = 3 to n = 2
- From n = 3 to n = 1
- From n = 2 to n = 1
Counting the Lines
Now, we can calculate the total number of unique transitions:
- From n = 4: 3 transitions (to n = 1, 2, 3)
- From n = 3: 2 transitions (to n = 1, 2)
- From n = 2: 1 transition (to n = 1)
When we add these transitions together, we get:
- 3 (from n = 4) + 2 (from n = 3) + 1 (from n = 2) = 6 transitions.
Conclusion
Thus, the total number of spectral lines emitted as the hydrogen atom transitions down from n = 4 is 6. Therefore, the correct answer is option 'D'.
When a hydrogen atom is excited to a higher energy level, it can emit light as it transitions back to lower energy levels. The principal quantum number (n) indicates the energy level; in this case, n = 4.
Calculating the Number of Spectral Lines
To determine the number of spectral lines emitted when an electron falls from level n = 4 to lower levels, we can use the following steps:
- Allowed Transitions: An electron can transition from n = 4 to n = 1, n = 2, and n = 3. Each transition emits a spectral line.
- Possible Transitions: The transitions from n = 4 can be summarized as follows:
- From n = 4 to n = 3
- From n = 4 to n = 2
- From n = 4 to n = 1
- From n = 3 to n = 2
- From n = 3 to n = 1
- From n = 2 to n = 1
Counting the Lines
Now, we can calculate the total number of unique transitions:
- From n = 4: 3 transitions (to n = 1, 2, 3)
- From n = 3: 2 transitions (to n = 1, 2)
- From n = 2: 1 transition (to n = 1)
When we add these transitions together, we get:
- 3 (from n = 4) + 2 (from n = 3) + 1 (from n = 2) = 6 transitions.
Conclusion
Thus, the total number of spectral lines emitted as the hydrogen atom transitions down from n = 4 is 6. Therefore, the correct answer is option 'D'.
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Hydrogen atom is excited from ground state to another state with principal quantum number equal to 4. Then the number of spectral lines in the emission spectra will be :a)2b)3c)5d)6Correct answer is option 'D'. Can you explain this answer?
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