Alpha-Particle Trajectory: Full Explanation
The trajectory of an alpha particle (He^2+, a helium nucleus with two protons and two neutrons)
is influenced by the Coulomb force when it encounters an atomic nucleus. This concept was crucial
in Rutherford's
alpha-particle scattering experiment, which led to the discovery of the atomic nucleus.
1. Forces Acting on an Alpha Particle
When an alpha particle approaches a positively charged nucleus, it experiences a repulsive
Coulomb force
due to electrostatic interaction. The force follows Coulomb's law:
F = (k * q1 * q2) / r^2
where:
- k is Coulomb's constant (8.99 × 10^9 Nm^2/C^2)
- q1 is the charge of the alpha particle (+2e)
- q2 is the charge of the nucleus (+Ze, where Z is the atomic number)
- r is the distance between the centers of the alpha particle and the nucleus.
2. Types of Alpha-Particle Trajectories
The trajectory of an alpha particle depends on its initial path and impact parameter (b), which is the
perpendicular distance between the initial path of the particle and the center of the nucleus.
(a) Direct Head-On Collision (Very Rare):
- If an alpha particle moves directly toward the nucleus (b = 0), it experiences maximum repulsion.
- The particle slows down, stops momentarily, and then is repelled straight back at 180 degrees.
(b) Close Approach with Large Deflection:
- If the particle comes close to the nucleus but not directly toward it, the Coulomb force repels it,
altering its path significantly.
- It gets deflected at large angles, sometimes close to 90 degrees or more.
(c) Distant Approach with Small Deflection:
- If the alpha particle is far from the nucleus (large b), it experiences a weak repulsive force.
- It is slightly deflected from its original path, usually by a few degrees.
The trajectory of an alpha particle (He^2+, a helium nucleus with two protons and two neutrons)
is influenced by the Coulomb force when it encounters an atomic nucleus. This concept was crucial
in Rutherford's
alpha-particle scattering experiment, which led to the discovery of the atomic nucleus.
1. Forces Acting on an Alpha Particle
When an alpha particle approaches a positively charged nucleus, it experiences a repulsive
Coulomb force
due to electrostatic interaction. The force follows Coulomb's law:
F = (k * q1 * q2) / r^2
where:
- k is Coulomb's constant (8.99 × 10^9 Nm^2/C^2)
- q1 is the charge of the alpha particle (+2e)
- q2 is the charge of the nucleus (+Ze, where Z is the atomic number)
- r is the distance between the centers of the alpha particle and the nucleus.
2. Types of Alpha-Particle Trajectories
The trajectory of an alpha particle depends on its initial path and impact parameter (b), which is the
perpendicular distance between the initial path of the particle and the center of the nucleus.
(a) Direct Head-On Collision (Very Rare):
- If an alpha particle moves directly toward the nucleus (b = 0), it experiences maximum repulsion.
- The particle slows down, stops momentarily, and then is repelled straight back at 180 degrees.
(b) Close Approach with Large Deflection:
- If the particle comes close to the nucleus but not directly toward it, the Coulomb force repels it,
altering its path significantly.
- It gets deflected at large angles, sometimes close to 90 degrees or more.
(c) Distant Approach with Small Deflection:
- If the alpha particle is far from the nucleus (large b), it experiences a weak repulsive force.
- It is slightly deflected from its original path, usually by a few degrees.
