What is Paschen Series?

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Grade Level:

Class 12

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Definition

What is it?

The Paschen series describes a set of spectral lines of hydrogen that occur when an electron in a hydrogen atom jumps from a higher energy level (n > 3) down to the third energy level (n=3). These transitions release energy in the form of photons, which fall into the infrared region of the electromagnetic spectrum.

Simple Example

Quick Example

Imagine a student, Rahul, climbing down stairs. If Rahul always stops at the third floor (n=3) after starting from any floor above it (4th, 5th, 6th floor etc.), the 'energy' released by his descent at each step would be like the photons of the Paschen series. Each jump from a different higher floor to the third floor gives a different 'energy packet' (photon).

Worked Example

Step-by-Step

Let's calculate the wavelength of the first line in the Paschen series (n=4 to n=3 transition) using the Rydberg formula.

Step 1: Identify the Rydberg formula: 1/λ = R * (1/n1^2 - 1/n2^2), where R is the Rydberg constant (1.097 x 10^7 m^-1).
---Step 2: For the Paschen series, the final energy level n1 is 3. For the first line, the initial energy level n2 is 4.
---Step 3: Substitute the values into the formula: 1/λ = 1.097 x 10^7 m^-1 * (1/3^2 - 1/4^2).
---Step 4: Calculate the squares: 1/λ = 1.097 x 10^7 m^-1 * (1/9 - 1/16).
---Step 5: Find a common denominator for the fractions: 1/λ = 1.097 x 10^7 m^-1 * (16/144 - 9/144).
---Step 6: Subtract the fractions: 1/λ = 1.097 x 10^7 m^-1 * (7/144).
---Step 7: Calculate the value: 1/λ = 1.097 x 10^7 * 0.04861 = 5.337 x 10^5 m^-1.
---Step 8: Find λ by taking the reciprocal: λ = 1 / (5.337 x 10^5 m^-1) = 1.874 x 10^-6 meters or 1874 nanometers.

Answer: The wavelength of the first line in the Paschen series is approximately 1874 nm.

Why It Matters

Understanding spectral series like Paschen is crucial for scientists studying the universe. It helps astronomers in ISRO and other space agencies identify elements in distant stars and galaxies, telling us what they are made of. This knowledge is also used in fields like materials science and spectroscopy to analyze the composition of various substances.

Common Mistakes

MISTAKE: Confusing the final energy level (n1) for Paschen series with other series like Balmer or Lyman. | CORRECTION: Remember, for Paschen series, the electron always lands on n=3. For Balmer, it's n=2, and for Lyman, it's n=1.

MISTAKE: Using the wrong Rydberg constant or forgetting to square the 'n' values in the formula. | CORRECTION: Always use R = 1.097 x 10^7 m^-1 and ensure you square n1 and n2 correctly (n1^2 and n2^2).

MISTAKE: Assuming Paschen series lines are visible light. | CORRECTION: Paschen series transitions result in infrared radiation, which is not visible to the human eye. Only the Balmer series has visible lines.

Practice Questions

Try It Yourself

QUESTION: What is the final energy level an electron lands on to produce a line in the Paschen series? | ANSWER: n=3

QUESTION: Which region of the electromagnetic spectrum do the lines of the Paschen series fall into? | ANSWER: Infrared region

QUESTION: An electron in a hydrogen atom jumps from n=5 to n=3. Is this transition part of the Paschen series? Explain. | ANSWER: Yes, it is part of the Paschen series because the electron transitions from a higher energy level (n=5) to the third energy level (n=3).

MCQ

Quick Quiz

For the Paschen series, what is the principal quantum number (n) of the lower energy level to which electrons transition?

n = 1

n = 2

n = 3

n = 4

The Correct Answer Is:

The Paschen series is defined by electron transitions where the electron lands on the third energy level (n=3). Options A, B, and D correspond to the Lyman, Balmer, and Brackett series, respectively.

Real World Connection

In the Real World

In astronomy, telescopes with special infrared detectors are used to observe light from distant stars and galaxies. When these telescopes detect specific infrared wavelengths corresponding to the Paschen series of hydrogen, scientists can confirm the presence of hydrogen in those celestial bodies, helping us understand the composition and evolution of the universe, much like how ISRO studies planetary atmospheres.

Key Vocabulary

Key Terms

SPECTRAL SERIES: A set of wavelengths of light emitted by atoms as electrons jump between specific energy levels. | ENERGY LEVEL: A specific orbit or shell where electrons can reside around an atom's nucleus. | PHOTON: A tiny packet of electromagnetic energy, like a 'light particle'. | INFRARED: A type of electromagnetic radiation with wavelengths longer than visible light, felt as heat. | RYDBERG FORMULA: A mathematical formula used to predict the wavelengths of light emitted by a hydrogen atom.

What's Next

What to Learn Next

Next, you should learn about the other hydrogen spectral series like the Lyman, Balmer, and Brackett series. Understanding these will help you see the complete picture of how electron transitions create different types of light and how they relate to the Paschen series.