Problem 156 - A Complete Resource Book in Chemistry for JEE Main

Question

In Bohr series of lines of hydrogen spectrum, the third line from the red end corresponds to which one of the following inter-orbit jumps of the electron for Bohr orbits in an atom of hydrogen? (a) \(3 \longrightarrow 2\) (b) \(5 \longrightarrow 2\) (c) \(4 \longrightarrow 1\) (d) \(2 \longrightarrow 5\)

Step-by-Step Solution

Answer

The third line corresponds to the electron transition from energy level 5 to 2, which is option (b).

Step 1: Understand the Problem

We need to find the electron transition in hydrogen corresponding to the third line from the red end. These spectral lines are the result of electron transitions to the second energy level (Balmer series) from higher levels.

Step 2: Recall the Balmer Series

The Balmer series consists of electron transitions from higher energy levels (such as 3rd, 4th, 5th, ...) to the second energy level. The series produces visible spectrum lines.

Step 3: Identify the Series' Third Line

The first line in the Balmer series is from energy level 3 to 2 (first line), the second line is from 4 to 2, and therefore, the third line is from 5 to 2.

Step 4: Match to Given Options

The transition corresponding to the third line from the red end of the spectrum is from energy level 5 to 2, matching option (b).

Key Concepts

Bohr Model

The Bohr Model is an essential concept to understand how electrons behave in atoms. It describes the atom as a small, positively charged nucleus surrounded by electrons that travel in circular orbits. These orbits are quantized, which means electrons can only occupy certain levels or paths. This model was a significant breakthrough by Niels Bohr and helped to explain why atoms emit light in specific spectra.
According to the Bohr Model:

• Electrons revolve in specific orbits with fixed energy levels.
• An electron in an orbit has a distinctive energy, and can only change orbits by absorbing or releasing energy equal to the difference in energy levels.
• It accounts for the Hydrogen atomic spectra by explaining electron transitions with quantized energy differences.

Despite its simplicity, the Bohr Model provides a foundational framework for understanding atomic structure and spectral lines. It lays the groundwork for more advanced quantum models.

Balmer Series

The Balmer Series is a part of the hydrogen emission spectrum where electron transitions end at the second energy level. This series is named after Johann Balmer, who discovered the linear formula that predicts the wavelengths of visible spectral lines of hydrogen. The Balmer Series specifically reveals why certain transitions of electrons between orbits produce visible light.
In detail, the Balmer Series:

• Contains transitions from higher energy levels (n = 3, 4, 5, ...) to the second energy level (n = 2).
• Results in the emission of light in the visible spectrum.
• The formula for calculating wavelength is: \[ \frac{1}{\lambda} = R_H \left( \frac{1}{2^2} - \frac{1}{n^2} \right) \]where \( \lambda \) is the wavelength, \( R_H \) is the Rydberg constant, and \( n \) is the principal quantum number of the higher energy level.

The Balmer Series plays a crucial role in fields like astrophysics, where analyzing spectra helps identify elemental compositions of stars.

Electron Transitions

Electron transitions refer to the movement of electrons between different energy levels within an atom. These transitions are pivotal in explaining the production of spectral lines. Each transition corresponds to emission or absorption of energy and is unique based on the energy levels involved.
Key points about Electron Transitions include:

• An electron jumps to a higher orbit when it absorbs energy, moving to an excited state.
• It moves back to a lower energy level when it releases energy, often emitting a photon.
• The energy of the emitted or absorbed light is directly related to the energy difference between the two levels, characterized by the equation: \[ \Delta E = E_2 - E_1 = hf \]where \( \Delta E \) is the change in energy, \( h \) is Planck's constant, and \( f \) is the frequency of the emitted photon.

Understanding electron transitions is essential as it helps explain not only atomic spectra but also the fundamental processes powering lasers, LEDs, and even photosynthesis.