Question

What key assumption of Bohr's model would a "Solar System" model of the atom violate? What was the theoretical basis for this assumption?

Short answer

Bohr's model violates the assumption that electrons continuously radiate energy in circular orbits. This was based on Planck's quantum theory.

Step-by-step solution

Understand Bohr's Key Assumption

Bohr's model of the atom assumes that electrons move in specific, quantized orbits around the nucleus without radiating energy. This is critical because, according to classical mechanics, an accelerating electron (moving in a circular path) should emit electromagnetic radiation and lose energy, causing it to spiral into the nucleus.

Identify the Solar System Model's Assumption

The 'Solar System' model of the atom draws an analogy with planets orbiting the sun, implying that electrons move in circular or elliptical orbits around the nucleus due to electrostatic forces, similar to gravitational forces in the solar system. In classical physics, this would mean continuous radiation of energy by the electrons.

Examine the Violation

The key violation is that the 'Solar System' model suggests continuous energy radiation by electrons, contradicting Bohr's assumption of non-radiating quantized orbits. As per classical electro-dynamics, electrons should lose energy and collapse into the nucleus, which does not happen in actual atoms.

Theoretical Basis of Bohr's Assumption

Bohr introduced quantization to explain why electrons in an atom do not spiral into the nucleus. He postulated that only certain ‘allowed’ orbits exist where electrons do not radiate energy. This idea was theoretically based on Planck’s quantum theory and the stability of the hydrogen atom.

Key concepts

quantized orbits

In Bohr's model, one of the most important concepts is that of quantized orbits. Unlike classical mechanics, which would suggest that electrons can occupy any orbit around the nucleus, Bohr proposed that electrons reside in specific, fixed orbits. These orbits have distinct energy levels, meaning the electron can only be in these orbits and nowhere in-between.
Think of it like stepping stones across a river. Electrons can only 'step' on certain stones, and not in the water. They don't emit radiation while in these fixed orbits, so they don't lose energy.
This concept was revolutionary, helping explain why atoms are stable and how they emit light in specific spectral lines.

classical mechanics

Classical mechanics, the branch of physics developed by Newton and others, deals with the motions of macroscopic objects. In the context of atoms, it would predict that electrons, which are accelerating due to their circular paths, should constantly emit electromagnetic radiation.
This emitted radiation means the electron should gradually lose energy and eventually spiral into the nucleus, causing the atom to collapse.
However, we know atoms are stable, thus classical mechanics couldn't fully explain atomic structure. This is where Bohr's quantized orbits provide an answer.

quantum theory

Quantum theory is the theoretical glue behind Bohr's model. Introduced by Max Planck and further developed by Einstein and others, it explains phenomena at the atomic and subatomic levels.
Bohr's concept of 'quantized orbits' is rooted in Planck’s quantum theory, which states energy is quantized and can only be emitted or absorbed in discrete amounts, called quanta.
This quantum approach resolved many issues classical mechanics couldn't, offering a framework for understanding atomic behavior, such as why electrons don't spiral into the nucleus.

electromagnetic radiation

Electromagnetic radiation refers to waves of electric and magnetic fields, such as light. In classical mechanics, accelerating charges, like electrons in circular orbits, emit this radiation and thus lose energy.
In Bohr's model, however, electrons in quantized orbits do not emit this radiation. This was a key innovation: electrons remain in stable orbits without losing energy.
When electrons jump between these orbits, they emit or absorb specific amounts of electromagnetic radiation, explaining atomic emission spectra.

Solar System model

The Solar System model likens the atom to a miniature solar system, with electrons orbiting the nucleus like planets around the sun. While this provides an intuitive image, the analogy has flaws.
According to classical mechanics, the electrons should constantly lose energy by emitting electromagnetic radiation and collapse into the nucleus.
Bohr's model corrected this by introducing quantized orbits, where electrons are stable and only emit or absorb energy when changing orbits, not continuously.
This provided a more accurate and stable representation of atomic structure, bridging the gap between classical mechanics and quantum theory.