Rutherford α-Particle Scattering Experiment &
Advanced MCQs
Comprehensive Review Notes & Advanced JEE-Advanced / Top-Tier BSc Level MCQs
1. Introduction & Historical Context
In 1911, under Ernest Rutherford's direction, Hans Geiger and Ernest Marsden executed experiments
firing high-energy alpha particles at ultra-thin metal foils to evaluate atomic layouts, completely rendering
J.J. Thomson's Plum Pudding model incorrect.
2. Experimental Setup & Observations
• Source: High energy $ lpha$-particles ($+2e$ charge, Helium nuclei).
• Foil: Gold foil stripped down to a microscopic thickness of $2.1 imes 10^{-7} ext{ m}$.
• Environment: Pure vacuum to negate extraneous molecular atmospheric scattering collisions.
• Statistics: ~99.9% pass straight without deviation; ~0.14% deflect $> 1^\circ$; ~1 in 8000 scatter
past $> 90^\circ$.
3. Analytical Core Equations
Coulombic Force: $F = rac{1}{4\pi arepsilon_0} rac{2Ze^2}{r^2}$
Distance of Closest Approach ($r_0$): Formulated via complete conversion of Initial Kinetic Energy
($K$) to Electrostatic Potential Energy ($U$) at a head-on trajectory ($b=0$):
$r_0 = rac{1}{4\pi arepsilon_0} rac{4Ze^2}{mv^2} = rac{1}{4\pi arepsilon_0} rac{2Ze^2}{K}$
Impact Parameter ($b$): $b = rac{1}{4\pi arepsilon_0} rac{Ze^2}{K} \cot\left( rac{ heta}{2} ight)$
Scattering Probability Density: $N( heta) \propto rac{1}{\sin^4( heta/2)}$
Advanced Multiple Choice Questions (MCQs)
Strictly matched to advanced conceptual thresholds (BSc 2nd Year / JEE-Advanced Level). Includes
explicit conceptual mapping for incorrect choices.
1
, Part A: Theoretical MCQs (Conceptual & Foundational Nuances)
Q1. When analyzing the classical Rutherford scattering formula, why is the effect of
screening by atomic electrons completely ignored during large-angle deflection
calculations?
A) Electrons are completely stripped from the gold atoms upon exposure to vacuum.
B) The impact parameters required for large-angle scattering are orders of magnitude
smaller than the Bohr radius, penetrating inside the cloud.
C) Alpha particles move faster than light in the metal grid, leading to Cherenkov shielding.
D) The electronic mass creates an exactly equal and opposite electrostatic momentum
vector neutralizing the pull.
Correct Answer: B
Explanation: Large-angle deflection requires the alpha particle to come extraordinarily close to the
nucleus ($10^{-14} ext{ m}$). Since the atomic electron cloud resides at much larger distances
(~$10^{-10} ext{ m}$), the alpha particle penetrates deep inside the electron shell, meaning the
enclosed charge is purely the positive nucleus.
Why others are wrong: A is incorrect as gold remains neutral inside the lattice; C is physically
impossible as particles cannot exceed the speed of light; D is false because light electrons cannot
counteract the immense nuclear field.
2
Advanced MCQs
Comprehensive Review Notes & Advanced JEE-Advanced / Top-Tier BSc Level MCQs
1. Introduction & Historical Context
In 1911, under Ernest Rutherford's direction, Hans Geiger and Ernest Marsden executed experiments
firing high-energy alpha particles at ultra-thin metal foils to evaluate atomic layouts, completely rendering
J.J. Thomson's Plum Pudding model incorrect.
2. Experimental Setup & Observations
• Source: High energy $ lpha$-particles ($+2e$ charge, Helium nuclei).
• Foil: Gold foil stripped down to a microscopic thickness of $2.1 imes 10^{-7} ext{ m}$.
• Environment: Pure vacuum to negate extraneous molecular atmospheric scattering collisions.
• Statistics: ~99.9% pass straight without deviation; ~0.14% deflect $> 1^\circ$; ~1 in 8000 scatter
past $> 90^\circ$.
3. Analytical Core Equations
Coulombic Force: $F = rac{1}{4\pi arepsilon_0} rac{2Ze^2}{r^2}$
Distance of Closest Approach ($r_0$): Formulated via complete conversion of Initial Kinetic Energy
($K$) to Electrostatic Potential Energy ($U$) at a head-on trajectory ($b=0$):
$r_0 = rac{1}{4\pi arepsilon_0} rac{4Ze^2}{mv^2} = rac{1}{4\pi arepsilon_0} rac{2Ze^2}{K}$
Impact Parameter ($b$): $b = rac{1}{4\pi arepsilon_0} rac{Ze^2}{K} \cot\left( rac{ heta}{2} ight)$
Scattering Probability Density: $N( heta) \propto rac{1}{\sin^4( heta/2)}$
Advanced Multiple Choice Questions (MCQs)
Strictly matched to advanced conceptual thresholds (BSc 2nd Year / JEE-Advanced Level). Includes
explicit conceptual mapping for incorrect choices.
1
, Part A: Theoretical MCQs (Conceptual & Foundational Nuances)
Q1. When analyzing the classical Rutherford scattering formula, why is the effect of
screening by atomic electrons completely ignored during large-angle deflection
calculations?
A) Electrons are completely stripped from the gold atoms upon exposure to vacuum.
B) The impact parameters required for large-angle scattering are orders of magnitude
smaller than the Bohr radius, penetrating inside the cloud.
C) Alpha particles move faster than light in the metal grid, leading to Cherenkov shielding.
D) The electronic mass creates an exactly equal and opposite electrostatic momentum
vector neutralizing the pull.
Correct Answer: B
Explanation: Large-angle deflection requires the alpha particle to come extraordinarily close to the
nucleus ($10^{-14} ext{ m}$). Since the atomic electron cloud resides at much larger distances
(~$10^{-10} ext{ m}$), the alpha particle penetrates deep inside the electron shell, meaning the
enclosed charge is purely the positive nucleus.
Why others are wrong: A is incorrect as gold remains neutral inside the lattice; C is physically
impossible as particles cannot exceed the speed of light; D is false because light electrons cannot
counteract the immense nuclear field.
2
