Problem 123 - A Complete Resource Book in Chemistry for JEE Main

Question

Which of the following factors induce larger angle of deflection in Rutherford's scattering experiment? (a) The initial kinetic energy of striking \(\alpha\)-particles must be large (b) The initial kinetic energy of striking \(\alpha\)-particles must be small (c) The nucleus to which the \(\alpha\)-particles are striking must have small atomic number (d) The nucleus to which the \(\alpha\)-particles are striking must have high atomic number

Step-by-Step Solution

Answer

Larger deflection is induced by (b) small kinetic energy and (d) high atomic number.

Step 1: Understand Rutherford's Experiment

Rutherford's scattering experiment involved firing alpha (b1) particles at a thin gold foil. By observing the deflection angles of these particles, scientists inferred the structure of the atom. Larger deflection angles indicate a greater force exerted on the b1 particles, often caused by the positively charged nucleus.

Step 2: Analyze Kinetic Energy Effects

The kinetic energy of the b1-particles determines their speed. Larger kinetic energy results in higher speed, reducing the time for interaction with the nucleus and thus generally causing smaller deflection angles. Conversely, smaller kinetic energy allows for greater deflection because the particles spend more time interacting with the electric field of the nucleus.

Step 3: Assess Atomic Number Influence

The atomic number of an element corresponds to the number of protons in the nucleus. A higher atomic number means a stronger positive charge, attracting the negatively charged b1-particles more strongly, potentially causing larger deflection angles. A lower atomic number has less positive charge and therefore less deflection.

Step 4: Determine Larger Deflection Inducers

From the analysis, smaller kinetic energy of b1-particles and higher atomic number of the nucleus increase deflection. Smaller kinetic energy results in more interaction time, while higher atomic number increases the attractive force, both leading to larger deflection angles.

Key Concepts

Alpha Particles

In Rutherford's scattering experiment, alpha particles were key to uncovering the atomic structure. These particles are helium nuclei, consisting of two protons and two neutrons. They possess a positive charge due to their protons, which becomes crucial when interacting with atoms. Alpha particles were chosen because their relatively large mass and charge make them highly suitable for scattering experiments.
Understanding their movement through materials allows us to infer the properties of the materials themselves. When they collide with a nucleus in the foil, the positive charge of both the nucleus and the alpha particles causes them to repel one another.
This repulsion results in the deflection of alpha particles, whose angled paths provide invaluable information about the atomic number and structure of the nucleus they encounter.

Atomic Number

The atomic number is fundamental in determining the behavior of alpha particles during Rutherford's experiment. The atomic number is the number of protons in the nucleus of an atom, which gives the nucleus its positive charge. A higher atomic number means more protons, therefore, a stronger positive charge.

• This strong positive charge significantly influences alpha particles, which also have a positive charge.
• When alpha particles approach a nucleus with a high atomic number, they experience a stronger repulsive force.
• This results in larger deflection angles as they bounce off the nucleus.

A lower atomic number, in contrast, implies fewer protons, leading to weaker repulsion and smaller deflection angles for the alpha particles.

Kinetic Energy

Kinetic energy is a key factor in Rutherford's scattering experiment, affecting how alpha particles interact with nuclei. Kinetic energy is the energy of motion; the faster a particle is moving, the more kinetic energy it possesses. In this experiment, the kinetic energy impacts the deflection angle of the alpha particles.

• Higher kinetic energy results in alpha particles traveling faster, reducing their interaction time with the nucleus, and leading to smaller deflection angles.
• Lower kinetic energy means slower-moving particles, which increases their interaction time with the nucleus’s electric field, allowing for larger deflection angles.

This relationship is crucial in understanding the necessary balance of speed and deflection in scattering experiments.

Deflection Angle

The deflection angle in quantum experiments like Rutherford’s is crucial for understanding atomic structure. The deflection angle indicates how much the alpha particles have been diverted from their initial path after interacting with the nucleus.
The angle of deflection provides insights into the characteristics of the nucleus and the kinetic properties of the alpha particles:

• Larger deflection angles suggest a significant interaction between the alpha particles and a high atomic number nucleus.
• Smaller deflection angles may indicate either that the alpha particles have high kinetic energy or are interacting with nuclei with a lower atomic number.

These angles, read from the trajectories of the particles, offer immense insights into the forces at play within an atom, aligning with the theory of a concentrated positive charge at its center.