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An orbital electron in the ground state of hydrogen has an angular momentum L1 and an orbital electron in the first orbit in the ground state of lithium (double ionised positively charged) has an angular momentum L2 .Then :
  • a)
    L1 = L2
  • b)
    L1 = 3L2
  • c)
    L2 = 3L1
  • d)
    L2 = 9L1
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
An orbital electron in the ground state of hydrogen has an angular mom...
Doubly ionised positively lithium ion is a hydrogen like atom :
 
which depends only on the value of n. Also for both n = 1.
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Most Upvoted Answer
An orbital electron in the ground state of hydrogen has an angular mom...
Understanding Angular Momentum in Hydrogen and Lithium
In quantum mechanics, the angular momentum of an electron in an atom is quantized and is given by the formula:
L = n * ħ
where:
- L is the angular momentum,
- n is the principal quantum number,
- ħ is the reduced Planck's constant.
Angular Momentum in Hydrogen
- For hydrogen (H), which has one electron:
- The ground state corresponds to n = 1.
- Therefore, L1 = 1 * ħ = ħ.
Angular Momentum in Lithium
- In the case of lithium (Li), when it is double ionized (Li2+), it has lost two electrons:
- The remaining single electron is in the first orbit, also with n = 1.
- Therefore, L2 = 1 * ħ = ħ.
Comparison of Angular Momentum
- From the calculations:
- L1 = ħ (for hydrogen)
- L2 = ħ (for lithium)
- Thus, we can conclude:
- L1 = L2
Conclusion
- The correct answer to the question is option 'A': L1 = L2.
- Both the ground state of hydrogen and the first orbit of double ionized lithium have the same angular momentum value, which is ħ.
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An orbital electron in the ground state of hydrogen has an angular momentum L1 and an orbital electron in the first orbit in the ground state of lithium (double ionised positively charged) has an angular momentum L2 .Then :a)L1 = L2b)L1 = 3L2c)L2 = 3L1d)L2 = 9L1Correct answer is option 'A'. Can you explain this answer?
Question Description
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