How does the hydrogen spectrum support the quantum model of atoms?

The hydrogen spectrum played a crucial role in supporting the quantum model of atoms because it revealed that electrons exist in discrete energy levels, not just anywhere around the nucleus. Here’s a step-by-step explanation:

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1. Observation: Discrete Lines

• When hydrogen gas is energized, it emits light.
• Passing this light through a prism produces the hydrogen emission spectrum, which shows distinct lines at specific wavelengths, rather than a continuous spectrum.
• These lines are grouped into series, like:
  • Lyman series (ultraviolet)
  • Balmer series (visible)
  • Paschen series (infrared)

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2. Problem for Classical Physics

• Classical physics predicted that electrons orbiting the nucleus should emit radiation continuously while spiraling inward, leading to a continuous spectrum, not discrete lines.
• But the hydrogen spectrum showed only specific lines, which classical models couldn’t explain.

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3. Bohr’s Quantum Model

• Niels Bohr proposed that:
  1. Electrons occupy specific energy levels (quantized orbits) around the nucleus.
  2. Electrons don’t radiate energy while in a fixed orbit.
  3. Light is emitted or absorbed only when an electron jumps from one energy level to another.
• The energy of the emitted light corresponds exactly to the difference between two energy levels, which explains the discrete lines in the hydrogen spectrum.

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4. Mathematical Support

• Bohr’s formula for the wavelengths of hydrogen’s spectral lines matched the observed lines perfectly, giving strong evidence for quantized energy levels.

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5. Significance

• The hydrogen spectrum confirmed that electrons are not free to have any energy, but exist in specific, quantized states.
• This observation was one of the first clear experimental proofs of quantum theory, laying the foundation for modern atomic physics.

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Analogy:
Think of electrons as stairs in a building: they can stand on one stair or jump to another, but they cannot stand in between steps. The light emitted is like the “click” you hear when moving between stairs, and the hydrogen spectrum shows those clicks.

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