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Q12.1(b):
Choose the correct alternative from the clues given at the end of the each statement: In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force.
Solution :
Step 1: Establishing the Theoretical Foundation
To analyze the equilibrium of electrons in atomic models, we must evaluate the force vectors acting upon them. According to Classical Electromagnetic Theory (specifically Maxwell’s equations), an accelerated charge must radiate energy. If an electron were in a "stable equilibrium," it would imply a state where the net force is zero and no energy radiation occurs, preventing the collapse of the atom. In contrast, any orbit characterized by constant change in velocity (acceleration) results in a non-zero net force.
Step 2: Analyzing J.J. Thomson's Plum Pudding Model
In the Thomson model, the positive charge is distributed uniformly throughout the sphere, and the electron is embedded within it. When the electron is displaced from its equilibrium position at the center, the positive charge distribution exerts a restoring force proportional to the displacement ($F = -kx$). [By Hooke's Law and Electrostatic Force Analysis]. At the center, the net force is zero, representing a position of stable equilibrium.
Step 3: Analyzing the Rutherford/Bohr Planetary Model
In the planetary model, electrons revolve around the nucleus in circular orbits. The force acting on the electron is the centripetal force provided by the electrostatic Coulomb force ($F_c = \frac{1}{4\pi\epsilon_0} \frac{Ze^2}{r^2}$). Since the electron is undergoing circular motion, its velocity vector is constantly changing direction. [By Newton’s Second Law of Motion ($F = ma$)], a change in velocity implies a net force directed toward the center of the orbit. Therefore, in the planetary model, the electron is never in equilibrium.
Step 4: Comparative Data Table
| Model | Force Status | Equilibrium Type |
|---|---|---|
| Thomson (Plum Pudding) | Zero (at center) | Stable Equilibrium |
| Rutherford/Bohr | Non-Zero (Centripetal) | Dynamic (Accelerated) |
Step 5: Visual Representation of Force Vectors
Step 6: Conclusion based on Clues
The first blank refers to the state where the electron is held by a restoring force in a static potential, characteristic of the Thomson model. The second blank refers to the state of constant acceleration in an orbital path, characteristic of the Rutherford model.
Final Solution: In the ground state of Thomson model electrons are in stable equilibrium, while in Rutherford model electrons always experience a net force.
More Questions from Class 12 Physics Atoms EXERCISES
- Q12.1(a): Choose the correct alternative from the clues given at the end of the each statement: (a) The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model.
- Q12.1(a): Choose the correct alternative from the clues given at the end of the each statement: The size of the atom in Thomson’s model is .......... the atomic size in Rutherford’s model.
- Q12.1(b): Choose the correct alternative from the clues given at the end of the each statement: (b) In the ground state of .......... electrons are in stable equilibrium, while in .......... electrons always experience a net force.
- Q12.1(c): Choose the correct alternative from the clues given at the end of the each statement: (c) A classical atom based on .......... is doomed to collapse.
- Q12.1(c): Choose the correct alternative from the clues given at the end of the each statement: A classical atom based on .......... is doomed to collapse.
- Q12.1(d): Choose the correct alternative from the clues given at the end of the each statement: (d) An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in ..........
- Q12.1(d): Choose the correct alternative from the clues given at the end of the each statement: An atom has a nearly continuous mass distribution in a .......... but has a highly non-uniform mass distribution in ..........
- Q12.1(e): Choose the correct alternative from the clues given at the end of the each statement: (e) The positively charged part of the atom possesses most of the mass in ..........
- Q12.1(e): Choose the correct alternative from the clues given at the end of the each statement: The positively charged part of the atom possesses most of the mass in ..........
- Q12.2: Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?
- Q12.2: Suppose you are given a chance to repeat the alpha-particle scattering experiment using a thin sheet of solid hydrogen in place of the gold foil. (Hydrogen is a solid at temperatures below 14 K.) What results do you expect?
- Q12.3: A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?
- Q12.3: A difference of 2.3 eV separates two energy levels in an atom. What is the frequency of radiation emitted when the atom make a transition from the upper level to the lower level?
- Q12.4: The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?
- Q12.4: The ground state energy of hydrogen atom is –13.6 eV. What are the kinetic and potential energies of the electron in this state?
- Q12.5: A hydrogen atom initially in the ground level absorbs a photon, which excites it to the $n = 4$ level. Determine the wavelength and frequency of photon.
- Q12.5: A hydrogen atom initially in the ground level absorbs a photon, which excites it to the ((n)) = 4 level. Determine the wavelength and frequency of photon.
- Q12.6(a): (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the $n = 1, 2$, and $3$ levels.
- Q12.6(a): (a) Using the Bohr’s model calculate the speed of the electron in a hydrogen atom in the ((n)) = 1, 2, and 3 levels.
- Q12.6(b): (b) Calculate the orbital period in each of these levels.
- Q12.6(b): (b) Calculate the orbital period in each of these levels.
- Q12.7: The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11}$ m. What are the radii of the $n = 2$ and $n = 3$ orbits?
- Q12.7: The radius of the innermost electron orbit of a hydrogen atom is ((5.3 \times 10^{-11})) m. What are the radii of the ((n)) = 2 and ((n)) = 3 orbits?
- Q12.8: A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
- Q12.8: A 12.5 eV electron beam is used to bombard gaseous hydrogen at room temperature. What series of wavelengths will be emitted?
- Q12.9: In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius $1.5 \times 10^{11}$ m with orbital speed $3 \times 10^{4}$ m/s. (Mass of earth = $6.0 \times 10^{24}$ kg.)
- Q12.9: In accordance with the Bohr’s model, find the quantum number that characterises the earth’s revolution around the sun in an orbit of radius ((1.5 \times 10^{11})) m with orbital speed ((3 \times 10^{4})) m/s. (Mass of earth = ((6.0 \times 10^{24})) kg.)
CBSE Solutions for Class 12 Physics Atoms
Chapters in CBSE - Class 12 Physics
- Electric Charges and Fields
- Electrostatic Potential and Capacitance
- Current Electricity
- Moving Charges and Magnetism
- Magnetism and Matter
- Electromagnetic Induction
- Alternating Current
- Electromagnetic Waves
- Ray Optics and Optical Instruments
- Wave Optics
- Dual Nature of Radiation and Matter
- Nuclei
- Semiconductor Electronics
- Communication Systems
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