In the given figure, the energy levels of hydrogen atom have been shown alongwith some transitions m

Q: Why is the transition from $n=\infty$ called the 'series limit'?

It is called the series limit because it represents the maximum possible energy (and thus the shortest possible wavelength or limit) that a photon can have within that specific spectral series. Any higher energy would mean the electron wasn't bound to the atom to begin with.

Q: How do I remember the order of the spectral series?

A common mnemonic is 'Loves Beer, Passionately Pours Drinks' for Lyman ($n=1$), Balmer ($n=2$), Paschen ($n=3$), Brackett ($n=4$), and Pfund ($n=5$).

Q: What does the 'continuum' represent in the diagram?

The continuum represents the state where the electron is no longer bound to the nucleus. Its energy is $0\text{ eV}$ or greater. It is effectively at an infinite distance ($n=\infty$) from the nucleus.

Q: Why are the energy values negative?

The negative sign indicates that the electron is bound to the nucleus. You would have to supply that much positive energy to free the electron (bring its energy to zero). The ground state is the most tightly bound, hence the most negative.

Q: Is transition E also part of the Lyman series?

Yes! Transition E goes from $n=2$ to $n=1$. Since its final state is $n=1$, it belongs to the Lyman series. Specifically, it is the first member of the Lyman series.

Question

In the given figure, the energy levels of hydrogen atom have been shown alongwith some transitions marked A, B, C, D and E. The transitions A, B and C respectively represent

Options:

(A) The first member of the Lyman series, third member of Balmer series and second member of Paschen series.

(B) The ionisation potential of hydrogen, second member of Balmer series and third member of Paschen series.

(C) The series limit of Lyman series, second member of Balmer series and second member of Paschen series.

(D) The series limit of Lyman series, third member of Balmer series and second member of Paschen series.

Sigma Percentile · Accepted Answer

### Decoding the Hydrogen Energy Level Diagram

Imagine you are looking at a ladder where the rungs get closer and closer together as you climb higher. This is exactly what the energy levels of a hydrogen atom look like! The lowest rung is the ground state ($n=1$), and as you go infinitely high, you reach the "continuum" where the electron is completely free from the nucleus.

When an electron jumps down from a higher rung to a lower rung, it releases energy in the form of a photon. Depending on which rung the electron finally lands on, we group these jumps into different "spectral series". Let's decode the transitions shown in our diagram.

### The Rules of the Game

Before we analyze the specific transitions, we need to establish the ground rules for naming them. The name of a spectral series is determined entirely by the **final energy state** ($n_f$) of the electron:
- If it lands on $n_f = 1$, it emits ultraviolet light and belongs to the **Lyman series**.
- If it lands on $n_f = 2$, it emits visible light and belongs to the **Balmer series**.
- If it lands on $n_f = 3$, it emits infrared light and belongs to the **Paschen series**.

Furthermore, the specific "member" or "line" of the series is determined by how far the electron jumped. A jump from the immediately adjacent higher level (e.g., $2 	o 1$) is the first member. A jump from two levels up (e.g., $3 	o 1$) is the second member, and so on. The ultimate jump, from $n = \infty$ (the continuum), is called the **series limit**.

### Analyzing the Transitions

Let's put our rules to the test with the transitions marked in the diagram.

**Transition A:**
Look closely at arrow A. It originates from the continuum ($n_i = \infty$) and plunges all the way down to the ground state ($n_f = 1$). Because it lands on $n=1$, it is undeniably part of the Lyman series. Since it comes from the highest possible state, it represents the maximum energy jump for this series. Therefore, Transition A is the **series limit of the Lyman series**.

**Transition B:**
Arrow B starts at $n_i = 5$ and terminates at $n_f = 2$. Landing on $n=2$ places it squarely in the Balmer series. To find out which member it is, we count up from the final state:
- $3 	o 2$ is the 1st member.
- $4 	o 2$ is the 2nd member.
- $5 	o 2$ is the 3rd member.
Thus, Transition B is the **3rd member of the Balmer series**.

**Transition C:**
Finally, arrow C begins at $n_i = 5$ and ends at $n_f = 3$. A final state of $n=3$ means this is a Paschen series transition. Let's count the members again:
- $4 	o 3$ is the 1st member.
- $5 	o 3$ is the 2nd member.
Consequently, Transition C is the **2nd member of the Paschen series**.

### The Final Verdict

By systematically applying the rules of Bohr's atomic model, we have identified each transition:
- **A** is the series limit of the Lyman series.
- **B** is the 3rd member of the Balmer series.
- **C** is the 2nd member of the Paschen series.

Matching our findings with the given choices, we can confidently conclude that **Option (d)** is the correct answer. Physics is beautiful when you know how to read its diagrams!

Animated Solution for Physics - Atoms and Nuclei: In the given figure, the energy levels of hydrogen atom have been shown alongwith some transitions marked A, B, C, D and E. The transitions A, B and C respectively represent

Select Answer:

Visualized Solution

Visualizing the Energy Levels

Rules for Naming Spectral Series

Analyzing Transition A

Analyzing Transition B

Analyzing Transition C

Final Conclusion

The Sigma Insight: Bohr's Atomic Model and Energy Levels

Decoding the Hydrogen Energy Level Diagram

The Rules of the Game

Analyzing the Transitions

The Final Verdict

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