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Structure of Atom - Limitation of Rutherford Model of Atom-advanced

Grade 9CBSE

Review the key concepts, formulae, and examples before starting your quiz.

🔑Concepts

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According to Rutherford's model, electrons revolve around the nucleus in circular orbits. This is analogous to the motion of planets around the Sun.

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Maxwell's Electromagnetic Theory states that any charged particle (like an electron) undergoing acceleration must continuously radiate energy in the form of electromagnetic waves.

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Circular motion is inherently an accelerated motion because the direction of velocity changes at every point. The magnitude of this acceleration is given by a=v2ra = \frac{v^2}{r}.

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If an electron radiates energy, its total energy decreases, and its orbital radius must gradually shrink. This would cause the electron to follow a spiral path towards the nucleus.

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Calculations based on classical physics suggest that the electron would spiral into the nucleus in approximately 10−810^{-8} seconds, causing the atom to collapse.

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The primary limitation of Rutherford's model is its inability to explain the stability of an atom, as matter is known to be highly stable in reality.

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The model also failed to explain the existence of discrete spectral lines. According to the model, an electron spiraling inwards should emit a continuous spectrum of radiation, which contradicts experimental observations.

📐Formulae

a=v2ra = \frac{v^2}{r}

Fc=mv2rF_c = \frac{m v^2}{r}

Fe=14πϵ0q1q2r2F_e = \frac{1}{4 \pi \epsilon_0} \frac{q_1 q_2}{r^2}

mv2r=14πϵ0Ze2r2\frac{m v^2}{r} = \frac{1}{4 \pi \epsilon_0} \frac{Z e^2}{r^2}

💡Examples

Problem 1:

Explain why the electron in a Rutherford atom is considered to be in an 'accelerated' state even if its speed is constant.

Solution:

In circular motion, velocity is a vector quantity. Even if the speed (magnitude) remains constant, the direction of the electron changes continuously at every point in the orbit. This change in direction constitutes acceleration, known as centripetal acceleration, defined by a=v2ra = \frac{v^2}{r}.

Explanation:

According to classical physics, any acceleration of a charged particle requires the emission of electromagnetic radiation.

Problem 2:

What would be the consequence if an electron lost energy continuously while revolving around the nucleus?

Solution:

If the electron loses energy, it can no longer maintain its original orbital radius. The electrostatic attraction from the nucleus would pull it closer, causing the radius rr to decrease. The electron would follow a spiral trajectory and eventually collide with the nucleus, leading to the destruction of the atom.

Explanation:

This is known as the 'stability paradox' of the Rutherford model, as it predicts atoms should be unstable, yet they are the stable building blocks of matter.

Limitation of Rutherford Model of Atom-advanced Class 9 Notes & Examples