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Class 12 Science (PCM)

Physics Part 2

Atoms

Atoms

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Study Action Plan (Sorted by Difficulty)
Alpha-Particle Scattering Experiment
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Photon Emission and Absorption in Hydrogen
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Bohr Radius and Allowed Orbit Radii
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Emission and Absorption Spectra
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Energy Levels and Spectra
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Hydrogenic Atoms
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Limitations of Bohr's Model
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Rutherford's Nuclear Model
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Thomson’s Plum Pudding Model
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De Broglie's Hypothesis and Wave-Particle Duality
Accuracy: 20%
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Energy Formula for Hydrogen Atom
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Failure of Rutherford Model
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Ground State, Excited State and Ionisation Energy
Accuracy: 50%
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Rutherford Scattering Observations
Accuracy: 50%
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Atomic Spectra and Line Spectrum
Accuracy: 67%
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Medium
Bohr's Quantization Postulates
Accuracy: 67%
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Impact Parameter and Scattering Angle
Accuracy: 67%
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Medium
Bohr's Model of the Hydrogen Atom
Accuracy: 75%
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Low
Distance of Closest Approach
Accuracy: 100%
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Low
Hydrogen Spectrum and Balmer Lines
Accuracy: 100%
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Difficulty Level:
Low

Learning Objectives

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  • Understand the historical development of atomic theory.
  • Explain the significance of J. J. Thomson's experiments in the context of atomic structure.
  • Describe the differences between Thomson's and Rutherford's models of the atom.
  • Analyze the limitations of Rutherford's model in explaining atomic stability and spectra.
  • Summarize Bohr's model of the hydrogen atom and its postulates.
  • Apply Bohr's quantization condition to calculate energy levels and transitions in hydrogenic atoms.
  • Discuss the implications of de Broglie's hypothesis on the wave nature of electrons.
  • Evaluate the applicability of Bohr's model to multi-electron atoms and its limitations.

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Revision Notes & Summary

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Chapter Twelve: Atoms

12.1 Introduction

  • By the nineteenth century, evidence supported the atomic hypothesis of matter.
  • In 1897, J. J. Thomson discovered that atoms contain negatively charged electrons, making them electrically neutral overall.
  • Thomson's model (1898): Positive charge is uniformly distributed, with electrons embedded like seeds in a watermelon (plum pudding model).
  • Subsequent studies revealed a different arrangement of charges.

12.2 Key Models of the Atom

Thomson's Model

  • Atom as a spherical cloud of positive charges with electrons embedded.

Rutherford's Model

  • Most mass and positive charge concentrated in a tiny nucleus.
  • Electrons revolve around the nucleus.
  • Issues with Rutherford's model:
    • Predicts instability due to spiraling electrons.
    • Cannot explain characteristic line spectra of different elements.

Bohr's Model

  • Proposed to explain line spectra and stability of hydrogenic atoms.
  • Introduced three postulates:
    1. Electrons revolve in stable orbits without emitting energy.
    2. Angular momentum is quantized: L = nh/2π (n = principal quantum number).
    3. Electrons can transition between orbits, emitting or absorbing photons.
  • Total energy quantized: Eₙ = -13.6 eV/n².
  • Ground state energy of hydrogen atom is -13.6 eV.

12.3 De Broglie's Explanation

  • De Broglie proposed that electrons have wave properties, explaining Bohr's quantization of angular momentum.
  • Standing waves form in electron orbits, leading to quantized energy levels.

12.4 Limitations of Bohr's Model

  • Applicable only to hydrogenic atoms; fails for multi-electron atoms.
  • Cannot explain relative intensities of spectral lines.

12.5 Summary of Key Points

  1. Atoms are electrically neutral, containing equal positive and negative charges.
  2. Thomson's model depicts a cloud of positive charge with embedded electrons.
  3. Rutherford's model has a nucleus with electrons revolving around it.
  4. Bohr's model introduces quantized orbits and energy levels for hydrogenic atoms.
  5. The wave nature of electrons explains quantization in Bohr's model.
  6. Bohr's model has limitations and is replaced by quantum mechanics for complex atoms.
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Practice Test – MCQs, True/False

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Multiple Choice Questions

A.

12.09 eV

B.

1.51 eV

C.

13.6 eV

D.

10.2 eV
Correct Answer: B

Solution:

The energy of the second excited state (n = 3) is -1.51 eV. To ionize the atom from this state, the energy required is 0 eV−(−1.51 eV)=1.51 eV0 \, \text{eV} - (-1.51 \, \text{eV}) = 1.51 \, \text{eV}.

Chapter Concept:

Ground State, Excited State and Ionisation Energy

A.

It accurately predicts the spectral lines of multi-electron atoms.

B.

It accounts for electron-electron interactions in multi-electron atoms.

C.

It fails to explain the relative intensities of spectral lines.

D.

It successfully describes the behavior of all elements.
Correct Answer: C

Solution:

Bohr's model fails to explain the relative intensities of spectral lines and does not account for electron-electron interactions in multi-electron atoms.

Chapter Concept:

Limitations of Bohr's Model

A.

Transition from n=3n=3 to n=2n=2

B.

Transition from n=4n=4 to n=3n=3

C.

Transition from n=2n=2 to n=1n=1

D.

Transition from n=5n=5 to n=4n=4
Correct Answer: C

Solution:

The transition from n=2n=2 to n=1n=1 involves the largest energy difference, resulting in the emission of a photon with the highest energy.

Chapter Concept:

Atomic Spectra and Line Spectrum

A.

The discovery of the neutron.

B.

The observation of alpha-particle scattering at large angles.

C.

The measurement of electron charge-to-mass ratio.

D.

The identification of isotopes.
Correct Answer: B

Solution:

The Plum Pudding Model was rejected after Rutherford's alpha-particle scattering experiment showed that a small fraction of alpha particles were deflected at large angles, indicating a concentrated positive charge in the nucleus.

Chapter Concept:

Thomson’s Plum Pudding Model

A.

It indicates that the electron is bound to the nucleus.

B.

It signifies that the electron is free from the nucleus.

C.

It shows that the electron has a negative charge.

D.

It implies that the electron is repelled by the nucleus.
Correct Answer: A

Solution:

The negative sign in the total energy indicates that the electron is bound to the nucleus and energy is required to remove it.

Chapter Concept:

Bohr's Model of the Hydrogen Atom

A.

The electron emits a photon with energy equal to the difference in energy levels.

B.

The electron absorbs a photon with energy equal to the difference in energy levels.

C.

The electron's angular momentum increases.

D.

The electron's speed decreases.
Correct Answer: A

Solution:

When an electron transitions from a higher energy level to a lower one, it emits a photon with energy equal to the difference between the two levels, as per Bohr's third postulate.

Chapter Concept:

Bohr Radius and Allowed Orbit Radii

A.

More alpha particles would be deflected at large angles.

B.

Fewer alpha particles would be deflected at large angles.

C.

The deflection pattern would be the same as with gold.

D.

Alpha particles would not be deflected at all.
Correct Answer: B

Solution:

Since hydrogen nuclei are much lighter than gold nuclei, fewer alpha particles would experience the large repulsive force necessary for large angle deflection.

Chapter Concept:

Alpha-Particle Scattering Experiment

A.

The electron's wave nature and standing wave condition.

B.

The electron's particle nature and gravitational forces.

C.

The electron's interaction with other electrons.

D.

The electron's magnetic properties.
Correct Answer: A

Solution:

Bohr's quantisation of angular momentum is explained by de Broglie's hypothesis that electrons exhibit wave nature, forming standing waves when the circumference of their orbit is an integral multiple of their wavelength.

Chapter Concept:

Photon Emission and Absorption in Hydrogen

A.

A photon is absorbed.

B.

A photon is emitted.

C.

The atom becomes ionized.

D.

The atom remains in the same state.
Correct Answer: B

Solution:

When a hydrogen atom transitions from a higher energy state to a lower energy state, a photon is emitted with energy equal to the difference between the two states.

Chapter Concept:

Photon Emission and Absorption in Hydrogen

A.

10.2 eV

B.

13.6 eV

C.

3.4 eV

D.

12.09 eV
Correct Answer: B

Solution:

The ionization energy of hydrogen, which is the energy required to remove the electron from the ground state, is 13.6 eV.

Chapter Concept:

Ground State, Excited State and Ionisation Energy

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True or False

Correct Answer: False

Solution:

Emission spectra contain bright lines due to photons emitted in downward transitions, whereas absorption spectra contain dark lines when atoms absorb photons of exact energies for upward transitions.

Chapter Concept :

Emission and Absorption Spectra

Correct Answer: True

Solution:

The experiment showed that a small fraction of alpha particles were deflected at large angles, indicating the presence of a dense nucleus.

Chapter Concept :

Alpha-Particle Scattering Experiment

Correct Answer: True

Solution:

Bohr's model is successful for hydrogen but fails for multi-electron atoms as it does not consider electron-electron interactions and cannot explain the relative intensities of spectral lines.

Chapter Concept :

Limitations of Bohr's Model

Correct Answer: True

Solution:

The initial kinetic energy of the alpha-particle is converted into electrostatic potential energy as it approaches the nucleus, allowing for the calculation of the distance of closest approach, which estimates the upper limit of nuclear size.

Chapter Concept :

Distance of Closest Approach

Correct Answer: True

Solution:

The impact parameter is the perpendicular distance of the initial alpha-particle path from the nucleus. A small impact parameter means the alpha-particle passes close to the nucleus, resulting in a large repulsive force and a large scattering angle.

Chapter Concept :

Impact Parameter and Scattering Angle

Correct Answer: True

Solution:

Bohr's second postulate states that the angular momentum of an electron revolving in a stable orbit is quantized and given by L=nh2πL = n\frac{h}{2\pi}, where nn is an integer.

Chapter Concept :

Bohr's Quantization Postulates

Correct Answer: True

Solution:

Thomson's model proposed that the positive charge was spread uniformly throughout the atom, with electrons embedded within it, similar to seeds in a watermelon.

Chapter Concept :

Thomson’s Plum Pudding Model

Correct Answer: True

Solution:

Rutherford's model suggests that electrons in orbit around the nucleus would continuously emit radiation due to their acceleration, losing energy and spiraling into the nucleus, which contradicts the observed stability of atoms.

Chapter Concept :

Failure of Rutherford Model

Correct Answer: True

Solution:

Emission spectra are characterized by bright lines because they are produced when electrons in atoms transition from higher to lower energy levels, emitting photons.

Chapter Concept :

Emission and Absorption Spectra

Correct Answer: True

Solution:

Bohr's second postulate defines stable orbits where the angular momentum is quantized as an integral multiple of h/2πh/2\pi. This is a fundamental aspect of Bohr's model.

Chapter Concept :

Bohr's Quantization Postulates

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