Revision: Atoms, Molecules and Nuclei Physics HSC Science (General) 12th Standard Board Exam Maharashtra State Board

The spectrum consisting of bright lines on a dark background, emitted when an atomic gas is excited at low pressure by passing an electric current through it, is called the Emission Line Spectrum.

• The collection of different spectral lines obtained due to transition of an electron in hydrogen atom from upper energy levels to lower energy levels is called the Hydrogen Spectrum.
• The hydrogen spectrum consists of specific wavelengths of light emitted by hydrogen atoms. When transition of an electron in a hydrogen atom occurs between energy levels, it emits or absorbs photons of certain wavelengths, creating a series of lines known as the hydrogen spectrum.

A new type of neutral particle whose mass is very nearly the same as that of a proton is called neutron.

A proton or a neutron is called a nucleon.

All nuclides with the same mass number are called isobars.

Nuclides with the same neutron number but different atomic number are called isotones.

Atomic species of the same element differing in mass are called isotopes.

A different mass unit used for expressing atomic masses is the atomic mass unit (u), defined as one-twelfth of the mass of a carbon-12 atom, called atomic mass unit.

Mathematically: 1 u = \[\frac{\text{mass of one }^{12}\mathrm{C~atom}}{12}\] = 1.660539 × 10⁻²⁷ kg

The nucleus of the lightest atom of hydrogen, which has a relative abundance of 99.985%, is called the proton.

A radioactive substance is a substance whose nuclei are unstable and therefore emit radiation on their own.

Electrons in outer orbits are weakly bound with the nucleus. In solids these weakly bound electrons leave their individual atom and become a part of it. These electrons are known as free electrons.

As nucleus is positively charged it strongly attracts the negative charged electrons. The electron orbit close to the nucleus are tightly bound by strong attractive force of nucleus. These electrons are known as bound electrons.

The phenomenon of spontaneous disintegration of an unstable nucleus of a naturally occurring isotope accompanied by emission of active radiations, α particles, β particles and γ radiations is called radioactivity.

Radioactivity is the spontaneous emission of high-energy radiation from the nucleus of an unstable atom.

One Becquerel (Bq) is defined as the activity of a quantity of radioactive samples in which one nucleus decays per second. It is the SI unit of the activity.

The attractive force which holds the nucleons together in the nucleus is called nuclear force.

`1/12`th of the mass of an atom of ₆C¹² isotope.

1 AMU is the average of proton rest mass and the neutron rest mass. Thus can be expressed as

1 AMU = 1.67377 × 10^-27 kg

= 1.67377 × 10^-24 gram

and C-12 is considered a reference for all atomic mass calculations.

Binding energy per nucleon is the average binding energy associated with each nucleon in the nucleus.

Mass defect is the difference between:

• the sum of the masses of the constituent protons and neutrons, and
• the actual mass of the nucleus.

The binding energy of a nucleus is the minimum energy required to separate the nucleus completely into its constituent protons and neutrons.

Thermonuclear fusion is fusion initiated by extremely high temperature, which gives nuclei enough kinetic energy to approach one another closely.

Nuclear fusion is the process in which light nuclei combine to form a more tightly bound heavier nucleus, and energy is released during the process.

Because both nuclei carry a positive charge, they repel each other through electrostatic force. This repulsion is called the Coulomb barrier in the context of fusion.

The property by which light or matter can show both wave-like and particle-like behaviour depending on the experiment is called wave-particle duality.

The waves associated with a moving material particle are called matter waves or de Broglie waves.

According to de Broglie, every moving particle is associated with a wave whose wavelength depends on its momentum.

If the distance between the alpha-particle and the nucleus is rr, then the electrostatic force between them is given by:

F = \[\frac {1}{4πε_0}\] ⋅ \[\frac{2e\cdot Ze}{r^2}\]

\[\Delta E=h\nu=E_i-E_f\]

\[\frac{1}{\lambda_{\mathrm{vac}}}=R_H\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]\]

where \[R_{H}=1.097\times10^{7}\mathrm{m}^{-1}\] (Rydberg constant)

m_p ​= 1.00727 u = 1.67262 × 10⁻²⁷ kg

m_n​ = 1.00866 u = 1.6749 × 10⁻²⁷ kg

A = Z + N

Where:

• Z = atomic number = number of protons.
• N = neutron number = number of neutrons.
• A = mass number = total number of protons and neutrons.

\[BE=\Delta m\cdot c^2\]

\[E=mc^2\]

\[\Delta m=[ZM_p+(A-Z)M_n]-M_\mathrm{nucleus}\]

\[\Delta m_a=Am_p+Bm_n+Am_e-M_{ar}\]

\[\Delta M=[Zm_p+(A-Z)m_n]-M\]

Where:

• ΔM = mass defect
• m_p​ = mass of one proton
• m_n​ = mass of one neutron
• M = actual mass of the nucleus

E_b ​= ΔMc²

Where:

• E_b​ = binding energy
• ΔM = mass defect
• c = speed of light

\[E_{bn}=\frac{E_b}{A}\]

Where:

• E_bn = binding energy per nucleon
• E_b​ = total binding energy of the nucleus
• A = mass number

For a particle of momentum p, the associated wavelength is:

For a particle of mass m moving with speed v:

1. The law states that the rate at which a radioactive substance undergoes decay is directly proportional to the number of undecayed nuclei present in the sample.
2. Mathematically: \[\frac {dN}{dt}\] ∝ N, which gives \[\frac {dN}{dt}\] = −λN, where λ is the decay constant.
3. On solving, the number of undecayed nuclei at time t is:
   N(t) = N₀e^−λt
   where N₀ is the number of nuclei present initially.
4. The time taken for the number of parent radioactive nuclei to reduce to half its value is called the half-life of the species, and the average life of a radioactive species is the average time a nucleus survives before it decays.

• Bohr accepted Rutherford’s nuclear model but modified it using quantum ideas.
• Classical mechanics and electromagnetism could not explain atomic-scale behaviour fully.
• Only certain orbits are allowed for the electron in the hydrogen atom.
• These orbits have definite total energy.
• Electron transitions between energy levels lead to photon emission.
• The energy of the hydrogen atom is negative because the electron is bound to the nucleus.

• Lyman series — transitions to n = 1; region: ultraviolet
• Balmer series — transitions to n = 2; region: visible
• Paschen series — transitions to n = 3; region: infrared
• Brackett series — transitions to n = 4; region: infrared
• Pfund series — transitions to n = 5; region: infrared
• The spectrum of hydrogen is important as most of the universe is made of hydrogen.
• Balmer series involves transitions starting/ending with the first excited state (n = 2) of hydrogen.

• Mass of ₆C¹² is exactly 12 amu; 1 amu = 1.660565 × 10⁻²⁷ kg.
• 1 amu of mass, when converted to energy, gives 931.5 MeV.
• Mass defect arises because some mass is converted into binding energy that holds the nucleus together.
• Atomic mass = Number of protons + Number of neutrons.
• There are three fundamental particles of an atom: protons, neutrons, and electrons.
• Protons and neutrons are big-sized particles present in the nucleus of an atom.
• The density of the nucleus is independent of the mass number of the atom.

Mass defect refers to the difference between the mass of a nucleus and the sum of the masses of its individual protons and neutrons (nucleons).

1.  The experiment verified the de-Broglie hypothesis.
2. In this experiment, the wave nature of electron particles was studied with the help of a nickel crystal.
3. Electrons undergo interference and diffraction phenomena and produce alternate bright and dark rings.
4. When accelerating potential V = 54 V:
   λ = 0.165 nm (Experimental value)
   λ = 0.167 nm (Theoretical value from de-Broglie hypothesis)