📘 Topic Description
Alpha-particle scattering experiment was performed by Ernest Rutherford and his collaborators using a thin gold foil. A beam of positively charged alpha particles was directed towards the foil and the scattered particles were detected on a fluorescent screen.
⭐ The experiment established that an atom contains a very small,
dense and positively charged nucleus surrounded by mostly empty space.
🔬 Rutherford Gold Foil Experiment
- Alpha particles were produced from a radioactive source.
- The particles were directed towards a very thin gold foil.
- A zinc sulphide screen detected scattered alpha particles.
- Most alpha particles passed straight through.
- Some particles suffered small deflections.
- A very small fraction suffered large deflections.
- A few particles were scattered almost backwards.
👀 Important Observations
Observation 1
Most alpha particles passed through the foil without deviation.
Observation 2
Some alpha particles were deflected through small angles.
Observation 3
Very few alpha particles were deflected through large angles.
Observation 4
An extremely small number were scattered backwards.
💡 Conclusions of Rutherford Experiment
- Most of the atom is empty space.
- Positive charge is concentrated in a tiny central region.
- Almost the entire mass of the atom is concentrated in the nucleus.
- The nucleus is extremely small compared with the size of the atom.
- Electrons revolve around the nucleus.
⚛️ Rutherford’s Nuclear Model
According to Rutherford's nuclear model:
- The atom contains a tiny positively charged nucleus.
- The nucleus contains almost the entire mass of the atom.
- Electrons revolve around the nucleus.
- The electrostatic attraction provides the centripetal force.
- Most of the atomic volume is empty space.
F = 1/(4πε₀) × (Zze²/r²)
For an alpha particle of charge +2e approaching a nucleus of charge +Ze, the electrostatic force is repulsive.
⚠️ Limitations of Rutherford Model
- Could not explain atomic stability.
- According to classical electromagnetic theory, revolving electrons should radiate energy.
- The electron would lose energy and spiral into the nucleus.
- Could not explain the discrete line spectra of atoms.
- Could not explain quantisation of energy.
🎯 Distance of Closest Approach
When a positively charged alpha particle approaches a positively charged nucleus head-on, electrostatic repulsion slows the alpha particle. At the closest point, its initial kinetic energy is completely converted into electrostatic potential energy.
K.E. = Electrostatic Potential Energy
½mv² = 1/(4πε₀) × (2Ze²/r₀)
Therefore:
⭐ r₀ = 1/(4πε₀) × (4Ze²/mv²)
Since the initial kinetic energy is:
K = ½mv²
the relation can also be written as:
⭐ r₀ = 1/(4πε₀) × (2Ze²/K)
For a head-on collision, the alpha particle reaches its maximum
distance of penetration and momentarily comes to rest.
📐 Impact Parameter
The impact parameter (b) is the perpendicular distance between the initial direction of motion of the alpha particle and the centre of the nucleus, if the alpha particle were to continue undeflected.
⭐ Impact Parameter = b
A smaller impact parameter produces a larger scattering angle, whereas a larger impact parameter generally produces a smaller scattering angle.
b ↓ → scattering angle ↑
b ↑ → scattering angle ↓
b ↑ → scattering angle ↓
📊 Rutherford Scattering Relation
For Coulomb scattering, the impact parameter and scattering angle are related qualitatively by:
b ∝ cot(θ/2)
Thus:
θ ↑ → b ↓
θ ↓ → b ↑
🎯 Interactive Rutherford Scattering Practical
🧪 Practical Interpretation
- Small b: Alpha particle passes close to nucleus.
- Small b: Strong Coulomb repulsion acts.
- Small b: Large scattering angle.
- Large b: Particle passes farther from nucleus.
- Large b: Smaller deflection.
- Head-on collision: Maximum scattering angle.
📊 Impact Parameter vs Scattering Angle
| Impact Parameter | Distance from Nucleus | Scattering | Scattering Angle |
|---|---|---|---|
| Very small | Very close | Very strong | Large |
| Medium | Moderate | Moderate | Moderate |
| Large | Far | Weak | Small |
| Zero | Head-on | Maximum | Maximum |
📝 MCQ Practice — 15 Questions
1. Rutherford's alpha-particle scattering experiment established the existence of:
A. Electron shell
B. Nucleus
C. Neutron
D. Photon
✔ Answer: B — Nucleus
2. Most alpha particles passed through the gold foil without deviation because:
A. Gold has no electrons
B. Atom is mostly empty space
C. Alpha particles have no charge
D. Nucleus is very large
✔ Answer: B
3. The charge of an alpha particle is:
A. +e
B. −e
C. +2e
D. −2e
✔ Answer: C
4. In a head-on collision, the scattering angle is:
A. Minimum
B. Zero
C. Maximum
D. Always 45°
✔ Answer: C
5. Impact parameter is represented by:
A. a
B. b
C. c
D. d
✔ Answer: B
6. If impact parameter decreases, scattering angle generally:
A. Decreases
B. Increases
C. Remains zero
D. Becomes negative
✔ Answer: B
7. The closest approach occurs when:
A. Potential energy is zero
B. Kinetic energy is maximum
C. Initial kinetic energy is converted into potential energy
D. Charge disappears
✔ Answer: C
8. The gold foil used by Rutherford was:
A. Thick
B. Very thin
C. Magnetic
D. Radioactive
✔ Answer: B
9. Large-angle scattering indicates that alpha particles pass:
A. Far from nucleus
B. Close to nucleus
C. Through empty space only
D. Outside the atom
✔ Answer: B
10. The nucleus is:
A. Negatively charged
B. Positively charged
C. Neutral
D. Without mass
✔ Answer: B
11. Almost all atomic mass is concentrated in:
A. Electron cloud
B. Nucleus
C. Empty space
D. Orbit
✔ Answer: B
12. The electrostatic force between alpha particle and nucleus is:
A. Attractive
B. Repulsive
C. Zero
D. Gravitational only
✔ Answer: B
13. If alpha-particle energy increases, its distance of closest approach for a head-on collision:
A. Increases
B. Decreases
C. Remains unchanged
D. Becomes infinite
✔ Answer: B
14. Rutherford model could not explain:
A. Nucleus
B. Empty space
C. Atomic stability
D. Positive charge
✔ Answer: C
15. The fluorescent screen in Rutherford's experiment was used to:
A. Produce alpha particles
B. Detect scattered alpha particles
C. Produce gold
D. Absorb radiation
✔ Answer: B
🟣 Assertion–Reason — 5 Questions
A. Both A and R are true and R is the correct explanation of A.
B. Both A and R are true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
B. Both A and R are true but R is not the correct explanation of A.
C. A is true but R is false.
D. A is false but R is true.
1. Assertion: Most alpha particles pass through gold foil without deflection.
Reason: Most of an atom is empty space.
Answer: A
Reason: Most of an atom is empty space.
Answer: A
2. Assertion: A small impact parameter produces a large scattering angle.
Reason: The alpha particle passes closer to the positively charged nucleus.
Answer: A
Reason: The alpha particle passes closer to the positively charged nucleus.
Answer: A
3. Assertion: The distance of closest approach decreases when alpha-particle kinetic energy increases.
Reason: Greater kinetic energy allows the alpha particle to approach closer before turning back.
Answer: A
Reason: Greater kinetic energy allows the alpha particle to approach closer before turning back.
Answer: A
4. Assertion: Rutherford's model could explain atomic stability completely.
Reason: A revolving charged particle should radiate energy according to classical electromagnetic theory.
Answer: D
Reason: A revolving charged particle should radiate energy according to classical electromagnetic theory.
Answer: D
5. Assertion: Head-on collision gives maximum scattering angle.
Reason: Its impact parameter is zero.
Answer: A
Reason: Its impact parameter is zero.
Answer: A
🟢 2 Marks — 6 Questions
Q1. What is meant by alpha-particle scattering?
Q2. Define impact parameter.
Q3. What is distance of closest approach?
Q4. Why did most alpha particles pass through the gold foil?
Q5. What is the charge on an alpha particle?
Q6. Why are large-angle deflections very rare?
🟡 3 Marks — 6 Questions
Q1. State three important observations of Rutherford's experiment.
Q2. Explain the concept of impact parameter.
Q3. Explain distance of closest approach.
Q4. Write three conclusions of Rutherford's experiment.
Q5. Explain why scattering angle increases when impact parameter decreases.
Q6. State three limitations of Rutherford's atomic model.
🟠 4 Marks — 6 Questions
Q1. Describe Rutherford's alpha-particle scattering experiment.
Q2. Explain Rutherford's nuclear model of atom.
Q3. Derive the expression for distance of closest approach.
Q4. Explain the relation between impact parameter and scattering angle.
Q5. Explain the significance of large-angle scattering.
Q6. Discuss the limitations of Rutherford's model.
🔴 5 Marks — 6 Questions
Q1. Explain Rutherford's alpha-particle scattering experiment with observations and conclusions.
Q2. Explain Rutherford's nuclear model and its limitations.
Q3. Derive the expression for distance of closest approach of an alpha particle.
Q4. Explain impact parameter and its effect on scattering angle.
Q5. Explain the significance of the observation that a few alpha particles were scattered backward.
Q6. Discuss the electrostatic interaction between an alpha particle and a nucleus.
🔵 6 Marks — 6 Questions
Q1. Describe Rutherford's alpha-particle scattering experiment in detail and explain all major observations.
Q2. Explain Rutherford's nuclear model, its assumptions, successes and limitations.
Q3. Derive the formula for distance of closest approach for a head-on collision.
Q4. Define impact parameter and explain its relationship with scattering angle using a suitable diagram.
Q5. Explain how Rutherford's experiment established that the nucleus is tiny, massive and positively charged.
Q6. Discuss alpha-particle scattering from a Coulomb field and explain the role of kinetic energy, impact parameter and closest approach.
🧮 Numerical Practice — 6 Questions
Q1. An alpha particle has kinetic energy K. Derive the expression
for its distance of closest approach to a nucleus of atomic number Z.
Q2. An alpha particle is directed head-on towards a gold nucleus.
If its kinetic energy is increased, explain quantitatively how the
distance of closest approach changes.
Q3. Calculate the distance of closest approach for an alpha particle
of known kinetic energy approaching a gold nucleus (Z = 79).
Q4. Two alpha particles have kinetic energies K and 4K.
Find the ratio of their distances of closest approach for the same nucleus.
Q5. An alpha particle approaches a nucleus with impact parameter b.
Explain how its scattering angle changes if b is reduced to half.
Q6. If the kinetic energy of an alpha particle is doubled, determine
the factor by which its distance of closest approach changes.
📌 Important Formula Revision
Coulomb Force
F = 1/(4πε₀) × Zze²/r²
Alpha Particle Charge
q = +2e
Closest Approach
r₀ = 1/(4πε₀) × 2Ze²/K
Using Velocity
r₀ = 1/(4πε₀) × 4Ze²/mv²
Impact Parameter
b = perpendicular distance
Scattering Relation
b ∝ cot(θ/2)
🚀 One-Minute Revision
🔹 Rutherford used alpha particles and a thin gold foil.
🔹 Most alpha particles passed straight through.
🔹 A small number were slightly deflected.
🔹 Very few suffered large deflections.
🔹 An extremely small number returned backwards.
🔹 Atom is mostly empty space.
🔹 Positive charge is concentrated in the nucleus.
🔹 Almost all atomic mass lies in the nucleus.
🔹 Alpha particle charge = +2e.
🔹 Head-on collision has b = 0.
🔹 Head-on collision gives maximum scattering angle.
🔹 Smaller b → larger scattering angle.
🔹 Larger b → smaller scattering angle.
🔹 Closest approach occurs when initial kinetic energy is converted into electrostatic potential energy.
🔹 Higher kinetic energy → smaller closest approach distance.
🔹 Most alpha particles passed straight through.
🔹 A small number were slightly deflected.
🔹 Very few suffered large deflections.
🔹 An extremely small number returned backwards.
🔹 Atom is mostly empty space.
🔹 Positive charge is concentrated in the nucleus.
🔹 Almost all atomic mass lies in the nucleus.
🔹 Alpha particle charge = +2e.
🔹 Head-on collision has b = 0.
🔹 Head-on collision gives maximum scattering angle.
🔹 Smaller b → larger scattering angle.
🔹 Larger b → smaller scattering angle.
🔹 Closest approach occurs when initial kinetic energy is converted into electrostatic potential energy.
🔹 Higher kinetic energy → smaller closest approach distance.
🔥 Important Search Keywords
Alpha Particle Scattering
Rutherford Experiment
Rutherford Nuclear Model
Gold Foil Experiment
Distance of Closest Approach
Impact Parameter
Rutherford Scattering
Alpha Particle
Nuclear Physics
Modern Physics
Class 12 Physics
CBSE Physics
JEE Physics
NEET Physics
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