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Structure of Atom - Limitations of Bohr's model-advanced

Grade 9CBSE

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

🔑Concepts

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Bohr's model is applicable only to single-electron species (hydrogen-like atoms) such as HH, He+He^{+}, Li2+Li^{2+}, and Be3+Be^{3+}. It fails to explain the spectra of multi-electron atoms.

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Bohr's model could not explain the 'Fine Structure' of spectral lines, where a single line is actually composed of several closely spaced lines when observed with high-power spectroscopes.

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It fails to explain the Zeeman Effect, which is the splitting of spectral lines in the presence of an external magnetic field.

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It fails to explain the Stark Effect, which is the splitting of spectral lines in the presence of an external electric field.

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Bohr's model treats the electron as a particle moving in a well-defined circular orbit (fixed path). This contradicts Heisenberg's Uncertainty Principle, which states that the exact position and momentum of an electron cannot be determined simultaneously.

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The model does not take into account the wave-particle duality of matter proposed by de Broglie. According to modern quantum mechanics, electrons exhibit wave-like properties, not just particle-like behavior.

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Bohr's model is a 2D representation (planar) of an atom, whereas modern science proves that atoms are 3D in nature.

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It could not explain the relative intensities of spectral lines (why some lines are brighter than others).

📐Formulae

mvr=nh2πmvr = \frac{nh}{2\pi}

En=−13.6×Z2n2 eVE_n = -13.6 \times \frac{Z^2}{n^2} \text{ eV}

Δx⋅Δp≥h4π\Delta x \cdot \Delta p \ge \frac{h}{4\pi}

λ=hmv\lambda = \frac{h}{mv}

rn=0.529×n2Z A˚r_n = 0.529 \times \frac{n^2}{Z} \text{ \AA}

💡Examples

Problem 1:

Which of the following species will Bohr's model fail to describe: HH, He+He^{+}, Li2+Li^{2+}, or HeHe?

Solution:

The Bohr model will fail to describe HeHe (neutral Helium).

Explanation:

Bohr's model is limited to single-electron systems. HH, He+He^{+}, and Li2+Li^{2+} all contain exactly 11 electron. However, neutral HeHe has 22 electrons, and Bohr's theory cannot account for the inter-electronic repulsions in multi-electron atoms.

Problem 2:

Calculate the angular momentum of an electron in the 2nd2^{nd} orbit of a Hydrogen atom according to Bohr's postulate.

Solution:

L=mvr=nh2πL = mvr = \frac{nh}{2\pi} For n=2n = 2: L=2h2π=hπL = \frac{2h}{2\pi} = \frac{h}{\pi} Substituting h≈6.626×10−34 J sh \approx 6.626 \times 10^{-34} \text{ J s}: L=6.626×10−343.14≈2.11×10−34 kg m2/sL = \frac{6.626 \times 10^{-34}}{3.14} \approx 2.11 \times 10^{-34} \text{ kg m}^2\text{/s}

Explanation:

Bohr postulated that angular momentum is quantized. A major limitation of this postulate is that it defines a fixed circular path, which contradicts the modern quantum mechanical view where electrons exist in 3D orbitals defined by probability.

Problem 3:

Why does the splitting of spectral lines in a magnetic field present a problem for Bohr's model?

Solution:

This phenomenon is known as the Zeeman Effect.

Explanation:

Bohr's model only considers the principal energy level (nn). It does not account for sub-shells or the magnetic properties of electron orientation. When an atom is placed in a magnetic field, the energy levels split further due to magnetic quantum numbers, which the Bohr model does not include in its framework.