Atoms And Nuclei: Key Concepts, Formulas, And Revision for NEET

Atoms and Nuclei are important topics in Physics for NEET. Atomic physics covers Thomson’s and Rutherford’s atomic models, Bohr’s model, the hydrogen spectrum, and excitation and ionisation energy. Understanding these concepts helps in learning atomic structure and energy levels.

Nuclear physics focuses on nuclear structure, mass defect, binding energy, radioactive decay, nuclear forces, fission, fusion, and nuclear reactors. This chapter also includes important formulas, shortcuts, and previous year questions (PYQs) to help you revise key concepts and practise numerical problems for NEET.

Atoms and Nuclei Overview

Atoms and Nuclei covers the structure of atoms, atomic models, energy levels, nuclear properties, and nuclear reactions. The following table provides an overview of the important topics, concepts, and formulas covered in these chapters for NEET.

Atomic Models

Atomic models explain how positive charge, negative charge, and mass are arranged inside an atom. Thomson’s and Rutherford’s models proposed different structures and helped scientists understand atomic structure. 

Thomson’s Plum-Pudding Model

J. J. Thomson proposed the plum-pudding model. Its main features were:

• The atom is spherical.

• Positive charge and mass are uniformly distributed throughout the atom.

• Electrons are embedded in the positively charged sphere.

• The atom is electrically neutral because the number of electrons equals the number of protons.

• Atomic size is of the order of 10^-10 metre.

Rutherford’s Alpha-Particle Scattering Experiment

Rutherford used a thin gold foil and alpha particles. About 99.8% of alpha particles passed without deviation, while a very small number were deflected.

He concluded that:

• Most of the atom is empty space.

• Nearly all the positive charge and mass are concentrated in a tiny nucleus.

• Electrons revolve around the nucleus.

• Nuclear size is of the order of 10^-15 metre.
  

Thomson’s model failed to explain alpha-particle scattering and atomic spectra. Rutherford’s model also failed to explain atomic stability because a revolving electron should continuously radiate energy and spiral into the nucleus.

Distance Of Closest Approach

When a positively charged alpha particle approaches a positively charged nucleus, electrostatic repulsion slows it down. At the closest point, its kinetic energy becomes zero, and its potential energy is maximum.

For an alpha particle of charge 2e approaching a nucleus of charge Ze:

Initial kinetic energy = electrostatic potential energy

r0 = 4kZe² / mv0²

If initial kinetic energy is K:

r0 = 2kZe² / K

Therefore:

r0 is proportional to Z / mv0²

It increases with nuclear charge and decreases with projectile mass, speed, or kinetic energy.

The impact parameter is the perpendicular distance between the original path of the alpha particle and the nucleus. For zero impact parameter, the particle approaches head-on and the scattering angle is 180 degrees.

Bohr’s Atomic Model

Bohr introduced stationary orbits to explain atomic stability and spectra.

Bohr’s Main Postulates

1. Electrons move only in permitted stationary orbits without radiating energy.

2. Angular momentum is quantised:

L = n h / 2 pi

where n = 1, 2, 3, and so on.

3. Radiation is emitted or absorbed when an electron changes its orbit:

Energy difference = h frequency = hc / wavelength

Emission occurs during a downward transition. Absorption occurs during an upward transition.

Important Bohr-Model Relations

For a hydrogen-like atom:

• Radius: r is proportional to n² / Z

• Speed: v is proportional to Z / n

• Angular momentum: L is proportional to n

• Total energy: E = -13.6 Z² / n² electron-volts

• Kinetic energy: K = 13.6 Z² / n² electron-volts

• Potential energy: U = -27.2 Z² / n² electron-volts

The energy relationship is:

K : U : E = 1 : -2 : -1

For hydrogen, the energy levels are:

• Ground state, n = 1: -13.6 electron-volts

• First excited state, n = 2: -3.4 electron-volts

• Second excited state, n = 3: -1.51 electron-volts

The radius of the second orbit is four times the first-orbit radius because r is proportional to n².

Hydrogen Spectrum

The wavelength of radiation emitted during a transition is given by:

1 / wavelength = RZ² [1 / nf² - 1 / ni²]

Here, ni is the initial orbit and nf is the final orbit.

The total number of possible spectral lines from the nth orbit is:

Number of lines = n(n - 1) / 2

The shortest wavelength corresponds to maximum energy and the largest energy gap. The longest wavelength corresponds to minimum energy and the smallest energy gap.

Ionization And Excitation Energy

Ionization energy is the energy required to remove an electron completely to infinity. Since energy at infinity is zero:

Ionization energy = magnitude of energy of the initial orbit

For hydrogen:

• From n = 1: 13.6 electron-volts

• From n = 2: 3.4 electron-volts

• From n = 3: 1.51 electron-volts

Excitation energy is the energy needed to move an electron from one orbit to a higher orbit. From n = 1 to n = 2:

Excitation energy = -3.4 - (-13.6) = 10.2 electron-volts

Nuclear Structure And Properties

The nucleus is approximately spherical. Its radius is:

R = R0 A^(1/3)

where A is the mass number.

Therefore:

• Nuclear volume is proportional to A.

• Nuclear surface area is proportional to A^(2/3).

• Nuclear density is nearly independent of A.

Nuclear density is approximately 10^17 kg per cubic metre.

Mass Defect And Binding Energy

The mass of separated protons and neutrons is greater than the mass of the bound nucleus. The difference is called mass defect.

Mass defect = mass of separated nucleons - mass of nucleus

Binding energy is the energy required to separate a nucleus completely into its nucleons:

Binding energy = mass defect × c²

When mass defect is expressed in atomic mass units:

Binding energy in MeV = mass defect × 931.5

For comparing nuclei of different sizes, use:

Binding energy per nucleon = total binding energy/mass number

A larger binding energy per nucleon generally means greater nuclear stability. The binding-energy-per-nucleon curve reaches its maximum near iron-56.

This explains:

• Fusion of light nuclei releases energy.

• Fission of heavy nuclei releases energy.

• Both processes move nuclei toward greater stability.

Radioactive Decay

Radioactive decay is the process in which an unstable atomic nucleus emits particles or energy to become more stable. Different types of decay affect the atomic number (Z) and mass number (A) in different ways. 

• Alpha Decay

An alpha particle contains two protons and two neutrons.

A to A - 4, and Z to Z - 2

Alpha decay occurs mainly in very heavy nuclei.

• Beta-Minus Decay

A neutron changes into a proton:

n becomes p + electron + antineutrino

A remains unchanged, while Z increases by one.

• Beta-Plus Decay

A proton changes into a neutron:

p becomes n + positron + neutrino

A remains unchanged, while Z decreases by one.

• Gamma Decay

An excited nucleus emits a photon:

Excited nucleus becomes ground-state nucleus + gamma photon

Neither A nor Z changes. Gamma decay changes only the energy state.

• Electron Capture

A proton captures an inner-shell electron and becomes a neutron:

p + electron becomes n

The atomic number decreases by one, while the mass number remains unchanged.

The penetrating power follows:

Gamma greater than beta greater than alpha

Nuclear Force

The nuclear force acts between nucleons over a very short range of about 1 femtometre. It is much stronger than the electrostatic and gravitational forces at nuclear distances.

Its important properties are:

• It is charge-independent.

• It acts between proton-proton, neutron-neutron, and proton-neutron pairs.

• It is attractive at normal nuclear separation.

• It becomes repulsive at extremely small separation.

• It does not follow the inverse-square law.

• It shows saturation, meaning a nucleon mainly interacts with nearby nucleons.

At large distances, nuclear force is negligible, while electrostatic force can act between protons.

Nuclear Fission, Fusion, And Reactors

Nuclear fission is the splitting of a heavy nucleus into smaller nuclei. Uranium-235 can undergo fission after absorbing a slow neutron. Approximately 200 MeV of energy and about 2.5 neutrons are released per fission.

Nuclear fusion is the combination of light nuclei to form a heavier nucleus. It requires temperatures near 10^7 K and occurs in the Sun. Fusion also powers the hydrogen bomb.

Nuclear Reactor Components

• Fuel rods: Contain fissile material such as uranium-235.

• Moderator: Slows fast neutrons. Heavy water is used as a moderator.

• Control rods: Absorb neutrons and regulate the reaction. Cadmium and boron are used.

• Coolant: Removes the heat produced by fission.

The moderator slows neutrons, while the control rod absorbs them. These functions must not be confused.

Reactor power is:

Power = total energy released / time

Using mass-energy equivalence:

Power = mass converted × c² / time

Common Mistakes to Avoid in Atoms and Nuclei

Students should focus on understanding atomic models, energy levels, nuclear properties, and radioactive decay. Using the correct formulas and remembering the differences between related concepts can help avoid errors while solving NEET Physics questions.

• Confusing atomic models: Remember the differences between Thomson’s and Rutherford’s models and their limitations.

• Using the wrong closest approach formula: Check the alpha particle’s mass, speed, and the nucleus’s charge.

• Ignoring the negative sign in Bohr energy: Bound electron energy is negative, while kinetic energy is positive.

• Confusing emission and absorption: Emission occurs during a downward transition, while absorption occurs during an upward transition.

• Mixing up spectral series: Lyman ends at (n=1), Balmer at (n=2), and Paschen at (n=3).

• Confusing excitation and ionisation energy: Excitation moves an electron to a higher level, while ionisation removes it completely.

• Mixing up isotopes, isobars, and isotones: Check whether atomic number, mass number, or neutron number is the same.

• Forgetting the mass defect conversion: Multiply the mass defect in atomic mass units by 931.5 to obtain binding energy in MeV.

Understanding atomic models, Bohr’s theory, nuclear properties, radioactive decay, and nuclear reactions helps build a strong foundation in Atoms and Nuclei. Revise the key formulas, shortcuts, and previous year questions to strengthen your NEET 2027 preparation.

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