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Which of the following transitions of He+ ion will give rise to spectral line which has same wavelength as some spectral line in hydrogen atom ?
  • a)
    n = 4to n = 2
  • b)
    n = 6to n = 5
  • c)
    n = 6to n = 3
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Which of the following transitions of He+ ion will give rise to spectr...
If n2 → n1 in H (z = 1) gives λ then z n2 → z n1 gives λ in H-like ion for He+ ion, z = 2
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Most Upvoted Answer
Which of the following transitions of He+ ion will give rise to spectr...
The correct answer is option 'A' - transition from n = 4 to n = 2.

Explanation:
- The wavelength of a spectral line in hydrogen atom is given by the Rydberg formula:
1/λ = R_H * (1/n1^2 - 1/n2^2)
where λ is the wavelength of the line, R_H is the Rydberg constant for hydrogen, and n1 and n2 are the principal quantum numbers of the initial and final states of the transition, respectively.
- We are looking for a transition in the helium ion (He+) that has the same wavelength as a spectral line in hydrogen.
- The energy levels of the helium ion are given by the formula:
E = -Z^2 * 13.6 eV / n^2
where Z is the atomic number (2 for helium) and n is the principal quantum number.
- By comparing the energy levels of hydrogen and helium ion, we can determine which transition in the helium ion corresponds to the same wavelength as a transition in hydrogen.
- The transition from n = 4 to n = 2 in the helium ion corresponds to the same energy difference as the transition from n = 3 to n = 2 in hydrogen.
- Therefore, the spectral line resulting from the transition from n = 4 to n = 2 in the helium ion will have the same wavelength as a spectral line in hydrogen.
- This is because the energy difference between the n = 3 and n = 2 states in hydrogen is the same as the energy difference between the n = 4 and n = 2 states in helium ion.
- Hence, the correct answer is option 'A' - transition from n = 4 to n = 2 in helium ion.
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Which of the following transitions of He+ ion will give rise to spectral line which has same wavelength as some spectral line in hydrogen atom ?a)n = 4to n = 2b)n = 6to n = 5c)n = 6to n = 3d)None of theseCorrect answer is option 'A'. Can you explain this answer?
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