Rutherford's Nuclear Model of an Atom | Physics Class 12 - NEET PDF Download

Thomson’s Atomic Model

Every atom is uniformly positive charged sphere of radius of the order of 10^-10 m, in which entire mass is uniformly distributed and negative charged electrons are embedded randomly. The atom as a whole is neutral.
Thomson's atomic model

Limitations of Thomson’s Atomic Model

• It could not explain the origin of spectral series of hydrogen and other atoms.
• It could not explain large angle scattering of α – particles.

Rutherford's Nuclear Model of an Atom

• In 1911, Rutherford, along with Geiger and Marsden, conducted the Alpha Particle scattering experiment.
• This experiment marked the inception of the 'nuclear model of an atom,' reshaping our understanding of atomic structure.

The Alpha Particle Scattering Experiment

• They conducted an experiment using a thin gold foil placed in the center of a rotatable detector made of zinc sulfide and a microscope.
• A beam of 5.5MeV alpha particles from a radioactive source was directed at the foil, collimated by lead bricks.
• Scattering of alpha particles could be observed by flashes on the screen post-collision.

Alpha Particle Scattering Experiment

Observations

• Majority of alpha particles passed through the foil without collisions.
• Approximately 0.14% of alpha particles scattered by more than 1 degree.
• Around 1 in 8000 alpha particles deflected by more than 90 degrees.

Conclusions and Arguments

• Results conflicted with Thomson's plum-pudding model of the atom.
• Rutherford proposed a concentrated positive charge at the atom's center based on deflection observations.

The Experiment by Rutherford

• Incident Alpha Particle and Deflection

  When the incident alpha particle approaches the positive mass at the center of the atom closely, it experiences repulsion, leading to deflection. Conversely, if it passes at a considerable distance from this mass, there is no deflection; it simply continues through.

• Nuclear Model of an Atom

  Rutherford proposed the 'nuclear model of an atom,' where the nucleus holds the entire positive charge and most of the mass. Electrons orbit around the nucleus similar to planets around the sun. He determined the nucleus size to be between 10^-15 and 10^-14 meters.

• Size Discrepancy and Atom Structure

  According to the Kinetic theory, the atom's size is approximately 10^-10 meters, making it 10,000 to 100,000 times larger than the nucleus suggested by Rutherford. Consequently, electrons should be positioned around 10,000 to 100,000 times the nucleus's size away from it.

• Empty Space in Atoms

  The experiment highlighted that most of an atom comprises empty space, explaining why a significant number of alpha particles passed through the foil. When alpha particles come close to the nucleus, they get deflected or scattered at wide angles. Since electrons have minimal mass, they do not alter the path of these incident alpha particles.

Alpha Particle Trajectory

• The path followed by an alpha particle is determined by the impact parameter of the collision. This parameter represents the perpendicular distance of each alpha particle from the center of the nucleus.
• When all alpha particles in a beam possess identical kinetic energy, their scattering behavior is solely influenced by the impact parameter.
• Alpha particles with a small impact parameter, i.e., those closer to the nucleus, undergo significant scattering, often at large angles.
• Conversely, alpha particles with a large impact parameter experience no deflection or scattering whatsoever.
• Alpha particles approaching with almost zero impact parameter, engaging in a head-on collision with the nucleus, bounce back.
• During the experimental observations conducted by Rutherford and his team, only a minute fraction of incident alpha particles exhibited rebounding behavior, implying that very few particles collided directly with the nucleus.
• This observation led to the inference that the mass of an atom is concentrated within an extremely small volume.

Distance of Closest Approach

r_o = 1 / 4π ε_o . 2Ze² / E_k

where, E_k = kinetic energy of the cc-particle.

Impact Parameter

The perpendicular distance of the velocity vector of a-particle from the central line of the nucleus, when the particle is far away from the nucleus is called impact parameter.

Impact parameter

where, Z = atomic number of the nucleus, E_k = kinetic energy of the c-particle and θ = angle of scattering.

Limitations of Rutherford Atomic Model

• About the Stability of Atom: According to Maxwell’s electromagnetic wave theory electron should emit energy in the form of electromagnetic wave during its orbital motion. Therefore. radius of orbit of electron will decrease gradually and ultimately it will fall in the nucleus.
• About the Line Spectrum: Rutherford atomic model cannot explain atomic line spectrum.