Comprehensive NEET Physics Notes for Atoms and Nuclei

Atoms

1. Introduction

By the nineteenth century, the atomic hypothesis of matter was well-supported. In 1897, J.J. Thomson discovered electrons, revealing that atoms have negatively charged components. Since atoms are neutral, they must also contain positive charges. Thomson proposed the "plum pudding model," where electrons are embedded in a positively charged sphere. This model was later replaced by Rutherford's nuclear model.

Did You Know?

The plum pudding model compared electrons to seeds in a watermelon, but this model was soon found to be incorrect.

2. Alpha-Particle Scattering and Rutherford’s Nuclear Model of Atom

2.1 The Experiment

In 1911, Geiger and Marsden, under Rutherford's guidance, conducted the alpha-particle scattering experiment. They directed a beam of alpha-particles at a thin gold foil and observed the scattering patterns.

Most particles passed through, but some deflected at large angles, suggesting a small, dense, positively charged nucleus.
Rutherford concluded that the nucleus contains most of the atom's mass and positive charge.

Common Misconception:

It is often thought that alpha particles easily penetrate the nucleus, but they actually scatter off due to the repulsive force of the nucleus.

2.2 Calculations and Implications

Rutherford's model led to the understanding that:

The nucleus is about 10^-15 m in size, while the atom is about 10^-10 m.
The nucleus contains protons and neutrons, while electrons orbit the nucleus.

3. Bohr’s Model of the Hydrogen Atom

3.1 Bohr’s Postulates

Niels Bohr modified Rutherford’s model by introducing quantum concepts:

Electrons revolve in stable orbits without radiating energy.
Orbits are quantized, with angular momentum given by $L = nh /2 π$ .
Electrons emit or absorb energy when transitioning between orbits, with the frequency given by $ν = (E_{i} - E_{f}) / h$ .

NEET Tip:

Remember Bohr's quantization rules for solving problems related to atomic spectra.

3.2 Energy Levels

The energy of an electron in the nth orbit is given by: $E_{n} = - 13.6/ n^{2}, e V$

The ground state (n=1) energy is -13.6 eV.
Higher states are progressively less negative, indicating higher energy.

Mnemonic:

"Higher n, higher energy" - As the principal quantum number n increases, the energy level rises.

4. Atomic Spectra

Atoms emit light at specific wavelengths, forming an emission spectrum. The spectrum of hydrogen, for instance, includes the Balmer series in the visible region.

Example:

The transition from n=3 to n=2 in hydrogen emits a photon of wavelength 656 nm (red light).

Real-life Application:

Spectral lines are used in astronomy to identify elements in stars.

5. Limitations of Bohr’s Model

While Bohr's model explained hydrogen spectra well, it had limitations:

It couldn’t predict spectra of atoms with more than one electron.
It didn't account for electron-electron interactions in multi-electron atoms.

Concept Connection:

Bohr's model was a stepping stone towards quantum mechanics, which provides a more comprehensive understanding of atomic structure.

Nuclei

1. Introduction

The nucleus, discovered by Rutherford, contains protons and neutrons. The number of protons (atomic number) defines the element, while the sum of protons and neutrons (mass number) determines its isotopes.

Did You Know?

Hydrogen has three isotopes: Protium (1 proton), Deuterium (1 proton + 1 neutron), and Tritium (1 proton + 2 neutrons).

2. Nuclear Forces

Nuclear forces are strong, short-range forces that hold protons and neutrons together in the nucleus, overcoming the repulsive electromagnetic force between protons.

Common Misconception:

Nuclear forces are often misunderstood as gravitational forces, but they are distinct and much stronger at short distances.

3. Radioactivity

3.1 Types of Radioactive Decay

Alpha Decay: Emission of an alpha particle (2 protons + 2 neutrons).
Beta Decay: Conversion of a neutron to a proton (or vice versa) with the emission of a beta particle (electron or positron).
Gamma Decay: Emission of gamma radiation (high-energy photons).

Example:

Uranium-238 undergoes alpha decay to form Thorium-234.

3.2 Half-Life

The half-life of a radioactive substance is the time taken for half of its atoms to decay. It is given by: $T_{1/2} = \frac{0.693}{λ}$ where $λ$ is the decay constant.

Real-life Application:

Carbon-14 dating is used to determine the age of archaeological samples.

4. Nuclear Reactions

4.1 Fission

Nuclear fission involves splitting a heavy nucleus into lighter nuclei, releasing a large amount of energy. Example: Uranium-235 fission in nuclear reactors.

4.2 Fusion

Nuclear fusion is the process where light nuclei combine to form a heavier nucleus, releasing energy. Example: Fusion of hydrogen nuclei in the sun to form helium.

NEET Problem-Solving Strategy:

Understand the mass-energy equivalence principle given by Einstein’s equation $E = m c^{2}$ to solve problems related to nuclear energy.

Practice Questions

Explain the difference between Thomson’s and Rutherford’s atomic models.
Derive the expression for the radius of an electron’s orbit in Bohr’s model.
Calculate the energy of an electron in the n=3 orbit of a hydrogen atom.
Define half-life and calculate the half-life of a substance with a decay constant of $0.693, d a y^{- 1}$ .
Describe the process of nuclear fusion and provide an example.

Answers to Practice Questions

Thomson’s model describes the atom as a positively charged sphere with embedded electrons, whereas Rutherford’s model has a dense nucleus with electrons orbiting around it.
Using Bohr’s quantization condition and Coulomb’s law, the radius of the nth orbit is given by: $r_{n} = \frac{n ^{2} h ^{2}}{4 π ^{2} m e ^{2}} ϵ_{0}$
The energy of an electron in the n=3 orbit is: $E_{3} = - \frac{13.6}{3 ^{2}}, e V = - 1.51, e V$
The half-life is: $T_{1/2} = \frac{0.693}{0.693 , d a y ^{- 1}} = 1, d a y$
Nuclear fusion involves combining light nuclei to form a heavier nucleus. Example: Two hydrogen nuclei fuse to form helium in the sun.

Glossary

Atom: The smallest unit of an element, consisting of protons, neutrons, and electrons.
Nucleus: The central part of an atom containing protons and neutrons.
Electron: A negatively charged particle orbiting the nucleus.
Proton: A positively charged particle in the nucleus.
Neutron: A neutrally charged particle in the nucleus.
Radioactivity: The spontaneous emission of radiation by unstable atomic nuclei.
Half-Life: The time taken for half of the radioactive atoms in a sample to decay.
Nuclear Fission: Splitting of a heavy nucleus into lighter nuclei, releasing energy.
Nuclear Fusion: Combining light nuclei to form a heavier nucleus, releasing energy.

Concept Connection

Link to NEET Physics: Atomic and Nuclear Physics Understanding atomic models and nuclear processes is essential for NEET Physics, as it forms the basis for numerous applications in medical imaging, energy production, and radiometric dating.