Hydrogen Spectral Series Table, Wavelengths, and Key Formulas
Spectral series in a hydrogen atom refer to a group of lines obtained when the electron transitions from higher energy levels to lower energy levels, emitting energy in the form of light. These emission lines are observed in the hydrogen spectrum and play a crucial role in understanding atomic structure in modern physics.
Each spectral series is named depending on the lower energy level (n1) where the electron comes to rest after transition. The pattern of lines is unique and forms only at specific wavelengths, highlighting the quantized nature of electron energies in a hydrogen atom.
Different Types of Spectral Series in Hydrogen Atom
When an electron in hydrogen transitions from a higher energy state (n2) to a lower energy state (n1), it emits a photon of light. The energy difference between these two states determines the wavelength of the emitted light, which appears as a line in the hydrogen spectrum. Each group of such transitions forms a series.
There are five main types of spectral series found in hydrogen. Each series corresponds to a unique final energy level (n1). Their names, final energy levels, typical transitions, and regions are explained below:
| Series Name | n1 (Lower Level) | Transitions From | Spectral Region |
|---|---|---|---|
| Lyman Series | 1 | n = 2, 3, 4, ... | Ultraviolet (UV) |
| Balmer Series | 2 | n = 3, 4, 5, ... | Visible |
| Paschen Series | 3 | n = 4, 5, 6, ... | Infrared (IR) |
| Brackett Series | 4 | n = 5, 6, 7, ... | Infrared (IR) |
| Pfund Series | 5 | n = 6, 7, 8, ... | Infrared (IR) |
The most important and visible series is the Balmer series. It is the only hydrogen spectral series that appears in the visible part of the electromagnetic spectrum, which is why it is often focused on in practical experiments.
Rydberg Formula for Spectral Series
The Rydberg formula helps to calculate the wavelength (λ) of any line in the hydrogen spectrum corresponding to the transition between higher and lower energy levels:
- R = Rydberg constant (1.097 × 107 m-1)
- n1 = lower energy level (fixed for each series)
- n2 = higher energy level (n2 > n1)
Step-by-Step Example: Calculating Balmer Line Wavelength
Let us calculate the wavelength of the first line in the Balmer series.
-
For the Balmer series, n1 = 2. The first line corresponds to n2 = 3.
-
Substitute in the formula:
1/λ = 1.097 × 107 (1/22 - 1/32)
= 1.097 × 107 (1/4 - 1/9) -
Calculate:
1/4 - 1/9 = (9 - 4) / 36 = 5/36
So, 1/λ = 1.097 × 107 × (5/36) -
λ = 36 / (1.097 × 107 × 5)
On simplifying, λ ≈ 656 nm. This value lies in the red region of the visible spectrum.
Spectral Series Data Table
| Series | n1 | Region | Visibility |
|---|---|---|---|
| Lyman | 1 | UV | Not visible |
| Balmer | 2 | Visible | Visible |
| Paschen | 3 | IR | Not visible |
| Brackett | 4 | IR | Not visible |
| Pfund | 5 | IR | Not visible |
Key Points and Summary
- Hydrogen emits energy as discrete lines when its electron moves from a higher to a lower energy level.
- The five named hydrogen spectral series are Lyman, Balmer, Paschen, Brackett, and Pfund.
- Each series is identified by the value of n1 (the final energy level).
- The Balmer series is visible to the human eye; all others are found in the UV or IR regions.
- Use the Rydberg formula with the correct n1 for series-specific wavelength calculations.
Further Learning and Practice
- For more explanations and solved problems, refer to Spectral Series on Vedantu.
- Practice calculating wavelengths for other series using the Rydberg formula for better understanding.
- Explore related topics such as the Bohr model and atomic structure for a complete foundation in modern physics.
FAQs on Spectral Series of Hydrogen Atom Explained for Students
1. Explain different types of spectral series in a hydrogen atom.
The spectral series of a hydrogen atom are groups of lines formed due to electron transitions from higher energy levels to a lower, fixed level. The main types are:
- Lyman Series: Electron falls to n1=1 from n2=2,3… (in ultraviolet region)
- Balmer Series: Electron falls to n1=2 from n2=3,4… (visible region)
- Paschen Series: Electron falls to n1=3 from n2=4,5… (infrared region)
- Brackett Series: Electron falls to n1=4 from n2=5,6… (infrared region)
- Pfund Series: Electron falls to n1=5 from n2=6,7… (infrared region)
Each series lies in a specific region of the electromagnetic spectrum and is defined by the value of the final level (n1).
2. What is the Rydberg formula, and how is it used for hydrogen spectrum calculations?
The Rydberg formula calculates the wavelength (λ) of emitted or absorbed light for transitions in hydrogen atoms:
1/λ = RH(1/n12 – 1/n22), where
RH = 1.097 × 107 m−1 (Rydberg constant),
n1 = lower energy level (depends on series),
n2 = higher energy level (n2 > n1).
- Select n1 for the desired series (e.g., Balmer: n1=2).
- Use n2=n1+1, n1+2, etc.
3. Which regions of the electromagnetic spectrum do the Lyman, Balmer, and Paschen series belong to?
Each spectral series appears in a specific region:
- Lyman Series: Ultraviolet (UV) region
- Balmer Series: Visible region (colors from violet to red)
- Paschen Series: Infrared (IR) region
4. Why are there multiple spectral series in hydrogen?
Multiple spectral series exist in hydrogen because electrons can transition down to different lower energy levels (n1=1, 2, 3, etc.) from higher excited states. Each set of transitions forms its own series, producing lines at distinct wavelengths in specific spectrum regions.
5. What are the principal quantum numbers (n1, n2) for each hydrogen spectral series?
For each series:
- Lyman: n1=1, n2≥2
- Balmer: n1=2, n2≥3
- Paschen: n1=3, n2≥4
- Brackett: n1=4, n2≥5
- Pfund: n1=5, n2≥6
6. What is the significance of the Balmer series in the hydrogen spectrum?
The Balmer series is significant because its lines fall within the visible region (410–656 nm), making them directly observable to the human eye. These lines are key for astrophysics and laboratory spectroscopy in identifying hydrogen and studying atomic transitions.
7. How do you calculate the wavelength of the first Balmer line in hydrogen?
To calculate the first Balmer line (H-α):
- Set n1=2 (Balmer), n2=3 (next higher level).
- Apply Rydberg formula: 1/λ = RH(1/2² – 1/3²)
- Solve: 1/λ = 1.097 × 107 (1/4 – 1/9) = 1.097 × 107 × (5/36)
- λ ≈ 656 nm (red line in visible spectrum)
8. What is meant by the term ‘spectral series’?
A spectral series is a set of related wavelengths produced when electrons in a hydrogen atom transition from higher energy levels to a fixed lower level, emitting photons with specific energies and forming characteristic lines in the atom’s spectrum.
9. Why are spectral lines important in Physics and Chemistry?
Spectral lines are important because they:
- Help identify elements in stars and laboratories (elemental fingerprint)
- Provide evidence for quantum energy levels
- Enable precise measurements of atomic structure and transitions
- Support models like Bohr’s atomic model
10. How do the Brackett and Pfund series differ from the Balmer series?
Brackett and Pfund series differ from the Balmer series in:
- Region: Both appear in the infrared (IR), while Balmer is visible
- n1 value: Brackett (n1=4), Pfund (n1=5); Balmer (n1=2)
- Applications: Used mainly in advanced spectroscopy and infrared astronomy, while Balmer is used in visible observations
11. Which spectral series of hydrogen is observed in the ultraviolet region?
The Lyman series is observed in the ultraviolet (UV) region. It involves electron transitions to the n1=1 energy level from higher levels (n2≥2). The wavelengths range from about 91 nm to 122 nm.
12. What is the typical exam weightage of questions on spectral series for JEE, NEET, and Boards?
Spectral series questions are asked annually in all major exams:
- JEE Main & Advanced: 1-2 MCQs or numericals per year
- NEET: 1-2 objective questions, focusing on wavelength, region, or formula
- Boards: Regular theory or calculation-based short answers (especially Balmer and Rydberg formula)
