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

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 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.

Radioactivity is a nuclear phenomenon. It is the process of spontaneous emission of α or β and γ radiations from the nucleus of atoms during their decay.

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.

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.

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.

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

Binding energy per nucleon is the least amount of energy required to liberate all of the nucleons from the nucleus.

As a result, the binding energy per nucleon is
`E_B/A`

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's model applies to one-electron species such as H, He⁺, Li²⁺, etc.

Postulates of Bohr's Model:

1. Electrons revolve in fixed circular paths called stationary states, orbits, shells, or energy levels. Each has a definite, fixed energy. Energy of the electron increases as it moves away from the nucleus.

2. Angular momentum of an electron is always an integral multiple of \[\frac{h}{2\pi}:\]
   \[mvr=n\cdot\frac{h}{2\pi}\]
   where m = mass, v = velocity, r = orbital radius, n = principal quantum number.

Energy is emitted or absorbed only when an electron jumps between energy levels — not while it is in a stationary orbit. When falling from higher (E₂) to lower (E₁) energy level:

\[\Delta E=E_2-E_1=h\nu=\frac{hc}{\lambda}\]

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)