which of the following would have a line spectrum similar to the line spectrum of hydrogen atom?
Which of the following would have a line spectrum similar to the line spectrum of hydrogen atom?
Answer:
To determine which atom or ion would have a line spectrum similar to that of a hydrogen atom, we first need to understand why the hydrogen atom exhibits its distinct line spectrum. Hydrogen atoms have a single electron, and the line spectrum corresponds to electron transitions between its quantized energy levels.
Key Concept:
- Hydrogen-like Ions:
- Atoms or ions with only one electron exhibit spectra similar to hydrogen because their energy levels are similarly quantized.
- Examples of such hydrogen-like ions are He⁺ (Helium ion), Li²⁺ (Lithium ion), Be³⁺ (Beryllium ion), etc.
Explanation:
For an ion to have a similar line spectrum to hydrogen, it must be hydrogen-like, meaning it has just one electron. This similarity arises because the energy levels in these systems scale proportionally with the nuclear charge as long as only one electron is present.
Potential Candidates:
-
He⁺ (Helium ion with one electron):
- Helium hydrogen-like ion, with similar quantized energy levels but adjusted for the increased nuclear charge (+2).
-
Li²⁺ (Lithium ion with one electron):
- Likewise, a lithium hydrogen-like ion would also follow this pattern, with adjusted energy levels for a nuclear charge of +3.
-
Be³⁺ (Beryllium ion with one electron):
- Similarly adjusted quantized energy levels for a nuclear charge of +4.
Algebraic Consideration:
The energy levels in a hydrogen-like atom or ion are given by:
E_n = - \frac{Z^2 \cdot R_H}{n^2}
where:
- Z is the atomic number.
- R_H is the Rydberg constant.
- n is the principal quantum number.
Therefore, He⁺, Li²⁺, and Be³⁺ have energy levels that are scaled versions of those in a hydrogen atom, but with Z^2 factored in. Hence, their spectral lines will be similar in nature but shifted due to the increased nuclear charge.
Conclusion:
Final Answer:
Any hydrogen-like ion (such as He⁺, Li²⁺, Be³⁺) would have a line spectrum similar to the line spectrum of the hydrogen atom due to their single-electron structures and similar quantized energy levels.
In summary, ions with only one electron, such as He⁺, Li²⁺, and Be³⁺, would show a line spectrum similar to the hydrogen atom. These ions are hydrogen-like and possess energy levels that depend on the nuclear charge and principal quantum number, resulting in spectra patterns that resemble that of hydrogen.