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Hydrogen atom excites energy level from fundamental state to \(n=3 .\) Number of spectrum lines, according to Bohr, is (a) 4 (b) 3 (c) 1 (d) 2

Short Answer

Expert verified
The number of spectral lines is 3.

Step by step solution

01

Identify Excited States

The hydrogen atom will transition from the ground state (n=1) to an excited state at n=3. We need to determine how many possible transitions can occur as the electron relaxes back to lower energy levels.
02

List Possible Transitions

The electron in n=3 can transition to n=2 and n=1, creating two possible transitions. Additionally, the electron in n=2 can transition to n=1, adding another possible transition. The transitions are 3 → 2, 3 → 1, and 2 → 1.
03

Count Spectrum Lines

Each transition corresponds to a spectral line. Therefore, we count the possible transitions: 3 → 2, 3 → 1, and 2 → 1. This results in three spectral lines.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Spectral Lines
Spectral lines are bright or dark lines that appear in an otherwise continuous spectrum of light. These lines occur due to the emission or absorption of light at specific wavelengths. When electrons move between different energy levels in an atom, they emit or absorb photons at particular wavelengths. This emission or absorption happens when an electron jumps to a lower or higher energy level, respectively. Each of these jumps corresponds to a unique spectral line, allowing scientists to identify the composition of distant stars and galaxies by observing the light they emit or absorb.
Electron Transitions
Electron transitions are movements of an electron between different energy levels in an atom. These transitions occur when the electron absorbs energy to move to a higher level or emits energy to drop to a lower level. The energy absorbed or emitted during these transitions is in the form of a photon. The photon's energy is equal to the difference between the two energy levels. A critical point to understand is that only certain transitions are allowed because the energy values of the levels are quantized. This means only specific electrons transitions occur, creating a unique set of emitted or absorbed wavelengths for each element.
Energy Levels
Energy levels are the distinct regions around an atom's nucleus where electrons are likely to be found. In Bohr's model of the hydrogen atom, these energy levels are quantized. This means each energy level corresponds to a fixed, calculable amount of energy. An electron in a lower energy level (closer to the nucleus) has less energy than one in a higher energy level (further from the nucleus). When an electron moves between these levels, it must gain or lose a specific, quantized amount of energy. This gain or loss manifests as the emission or absorption of a photon, linking energy levels directly to the formation of spectral lines. Understanding energy levels is crucial for explaining many phenomena in physics, such as atomic emission spectra and the chemical behavior of elements.

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