Define the term atomic number.
The number of protons in the nucleus is known as the atomic number of the element and is denoted by Z.
The number of protons in the nucleus of an atom, which is characteristic of a chemical element and determines its place in the periodic table. Atomic number is also equal to the number of electrons in an atom.
Define the term mass number.
The total number of neutrons and protons in the nucleus is called the mass number of the element and is denoted by A.
The atomic number of an atom is equal to the number of protons in its nucleus (which is same as the number of electrons in a neutral atom).
The mass number of an atom is equal to the total number of nucleons (i.e., the sum of the number of protons and the number of neutrons) in its nucleus.
When white light from a source passes through an atomic gas or vapour, the gas absorbs radiation of certain wavelengths. As a result, dark lines appear in the otherwise continuous spectrum. This type of spectrum is called an absorption spectrum.
When an atomic gas or vapour at low pressure is excited, it emits radiation of certain wavelengths. The emitted radiation, when analysed with a spectroscope, shows a series of bright lines on a dark background. This type of spectrum is called an emission line spectrum.
Define the term Nucleons.
The nucleus is made up of protons and neutrons, with protons having a positive charge and neutrons being neutral. Nucleons are made up of protons and neutrons.
The atoms of the same element, having same atomic number Z, but different mass number A, are called isotopes.
OR
Atoms having the same atomic number (Z) but different mass numbers (A).
The nuclear radius is the effective distance from the centre of the nucleus to its outer boundary. Since the nucleus does not have a perfectly sharp surface, this radius is treated as an approximate effective value in physics.
The splitting of a heavy nucleus into lighter nuclei, releasing energy.
Energy is released when nuclei undergo reactions (fission or fusion) that move them from a state of lower total binding energy to a state of higher total binding energy.
The combination of light nuclei to form a heavier nucleus, releasing energy.
The binding energy of a nucleus is the minimum energy required to separate the nucleus completely into its constituent protons and neutrons.
Binding energy per nucleon is the average binding energy associated with each nucleon in the nucleus.
Mass defect is the difference between:
The spontaneous emission of an electron (β⁻-decay) or a positron (β⁺-decay) from a radioactive nucleus is called β-Decay.
When a nucleus in an excited state spontaneously decays to its ground state and a photon is emitted with energy equal to the difference in the two energy levels of the nucleus, this is called γ-Decay.
The difference in the energy equivalent of the mass of the parent atom and that of the sum of masses of the products is called the Q-Value of the decay.
Define half-life period.
The half-life of a reaction is the time it takes for a reactant’s concentration to decrease to half of its initial value.
The nuclear phenomenon in which an unstable nucleus undergoes decay with the emission of some particles (α, β) and electromagnetic radiation (γ-rays) is called Radioactive Decay.
The rate of decay, i.e., the number of decays per unit time \[\left(-\frac{dN(t)}{dt}\right)\], is called Activity A(t).
The arithmetic average of the lives of all the nuclei present initially is called the Average Life of a radioactive element.
The time in which half the substance (radioactive) is disintegrated is called the Half-Life Period of a radioactive substance.
The phenomenon of emission of a nucleus of helium (2He4) from a radioactive nucleus is called α-Decay.
Define one Becquerel.
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.
Protons and neutrons together are called nucleons.
Atoms having the same mass number (A) but different atomic numbers (Z).
Atoms having the same number of neutrons (N) but different atomic numbers (Z).
The emission of a positron due to conversion of a proton into a neutron inside the nucleus is called beta plus (β⁺) decay.
\[_Z^AX\to_{Z-1}^AY+e^++\mathrm{neutrino}\]
The emission of an electron due to the conversion of a neutron into a proton inside the nucleus is called beta minus (β⁻) decay.
\[{}_Z^AX\to{}_{Z+1}^AY+e^-+\text{antineutrino}\]
Q = [mX − mY − me]c2
The emission of high-energy photons from an excited nucleus without a change in mass number or atomic number is called gamma decay.
\[_Z^AX^*\to_Z^AX+\gamma\]
The difference between the mass of the parent atom and the total mass of the decay products, expressed in energy terms, is called the Q-value of the decay.
The emission of an alpha particle (helium nucleus) from a heavy nucleus is called alpha decay.
\[{}_Z^AX\to{}_{Z-2}^{A-4}Y+{}_2^4He\]
Q = [mX − mY − mHe]c2
The difference between the total mass of individual nucleons and the actual mass of the nucleus.
ΔM = Zmp + Nmn − M
The average time for which a radioactive nucleus exists before decay is called the mean (average) life τ.
τ = \[\frac {1}{λ}\]
The process in which a heavy nucleus splits into two lighter nuclei with the release of energy is called nuclear fission.
A self-sustaining sequence of fission reactions in which neutrons produced in one fission cause further fissions is called a chain reaction.
A device in which nuclear fission is carried out in a controlled manner to produce energy is called a nuclear reactor.
The time required for the number of radioactive nuclei to reduce to half of its initial value is called the half-life T1/2.
\[\frac{N_0}{2}=N_0e^{-\lambda T_{1/2}}\]
\[T_{1/2}=\frac{\ln2}{\lambda}=\frac{0.693}{\lambda}\]
The nucleus formed after radioactive decay is called the daughter nucleus.
The original unstable nucleus which undergoes decay is called the parent nucleus.
The spontaneous transformation of an unstable nucleus into a more stable nucleus by emission of particles or radiation is called radioactive decay.
The force that binds protons and neutrons (nucleons) inside the nucleus is called the nuclear force or strong force.
The energy required to completely separate the nucleons of a nucleus and take them to infinity.
The process in which two light nuclei combine to form a heavier nucleus with the release of energy is called nuclear fusion.
The smallest indivisible particles of matter proposed by early philosophers are called atoms.
The central, tiny, positively charged part of an atom that contains almost all of its mass is called the nucleus.
The spontaneous disintegration of an unstable nucleus accompanied by emission of radiation is called radioactive decay.
The negatively charged particles discovered by J. J. Thomson are called electrons.
The atomic model proposed by J. J. Thomson in which an atom is considered as a uniformly positively charged sphere with electrons embedded in it is called Thomson’s atomic model. Thomson’s atomic model is also called the plum-pudding model.
An atom having equal total positive and negative charges and therefore having no net charge is called an electrically neutral atom.
The groups of spectral lines arranged according to a pattern are called spectral series (such as Lyman series, Balmer series, Paschen series, etc.).
The circular paths in which electrons revolve around the nucleus without emitting radiation are called stable orbits (stationary states).
The condition that the angular momentum of an electron in a stable orbit is an integral multiple of \[\frac {h}{2π}\] is called Bohr’s quantization condition.
The process in which an electron moves from one orbit to another with emission or absorption of a photon is called an electronic transition.
The positive integer nnn that determines the orbit of an electron is called the principal quantum number.
The spectrum obtained when a hot gas emits radiation at only certain specific wavelengths is called a line spectrum.
The bright lines seen in the spectrum due to emission of radiation at specific wavelengths are called emission lines.
The radius of the first orbit of the hydrogen atom (n = 1) is called the Bohr radius.
The lowest energy state of an atom (n = 1) is called the ground state.
The higher energy states (n > 1) are called excited states. The minimum energy required to raise an electron from the ground state to a higher energy state is called the excitation energy.
The constant appearing in the spectral formula of hydrogen is called the Rydberg constant.
RH = \[\frac{m_{\mathrm{e}}e^{4}}{8c\varepsilon_{0}h^{3}}=1.097\times10^{7}\mathrm{m}^{-1}\]
The ionisation energy of an atom is the minimum amount of energy required to be given to an electron in the ground state of that atom to set the electron free.
\[h\nu=E_2-E_1=\frac{hc}{\lambda}\]
\[L=mvr=\frac{nh}{2\pi},\quad n=1,2,3\ldots\]
The experimentally observed relation is: R = R0A1/3
where:
For nuclei,
R0 ≈ 1.2 × 10−15 m.
Eb = ΔMc2
Where:
\[\Delta M=[Zm_p+(A-Z)m_n]-M\]
Where:
\[E_{bn}=\frac{E_b}{A}\]
Where:
Q = [Mparent − Mproducts]c2
Q = [mX − mY − mHe]c2
Q = [mX − mY − me]c2
mvr = \[\frac {nh}{2π}\]
where
\[\rho=\frac{mA}{\frac{4}{3}\pi R^3}\]
After substituting R = R0A1/3:
\[\rho=\frac{3m}{4\pi R_0^3}\]
EB = ΔMc2
Binding Energy in terms of Protons and Neutrons:
EB = (Zmp + Nmn − M)c2
Binding Energy using Atomic Masses:
EB = [ZmH + Nmn − M]c2
Q = [Mass of reactants − Mass of products]c2
Example used in fusion inside the Sun:
Q = [4mp − mα − 2me]c2
Q = [mparent − mproducts]c2
Example form used in fission:
Q = [mU − m1 − m2 − (neutron masses)]c2
\[r_n=a_0\frac{n^2}{Z}\]
\[\frac{1}{\lambda}=R\left(\frac{1}{n^2}-\frac{1}{m^2}\right)\]
Bohr's First Postulate:
An atom consists of a small, massive central core called the nucleus, around which planetary electrons revolve. The centripetal force required for their rotation is provided by the electrostatic attraction between the electrons and the nucleus.
Bohr's Second Postulate (Quantum Condition):
The electrons are permitted to circulate only in those orbits in which the angular momentum of an electron is an integral multiple of \[\frac{h}{2\pi}\]; h being Planck's constant.
Bohr's Third Postulate:
While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.
Bohr's Fourth Postulate:
An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher to a lower orbit or from a lower to a higher orbit, respectively.
The rate of decay of a radioactive substance at any instant is directly proportional to the number of undecayed nuclei present at that instant.
Let N (t) be the number of undecayed nuclei at time t.
The rate of decay is proportional to N (t):
\[\frac {dN}{dt}\] ∝ -N (t)
Introducing proportionality constant λ (decay constant):
\[\frac{dN}{dt}=-\lambda N(t)\]
Separating variables:
\[\frac{dN}{N}=-\lambda dt\]
Integrating from N0 at t = 0 to N at time t:
\[\int_{N_0}^N\frac{dN}{N}=-\lambda\int_0^tdt\]
\[\ln\left(\frac{N}{N_0}\right)=-\lambda t\]
\[N=N_0e^{-\lambda t}\]
This is the Radioactive Decay Law.
Radioactive decay follows an exponential law. The number of undecayed nuclei and the activity decrease exponentially with time. The half-life and mean life are constants characteristic of a given radioactive substance and depend only on the decay constant λ\lambdaλ.
Isotopes are atoms of the same element that have the same atomic number but different mass numbers (different number of neutrons).
Same in isotopes:
Different in isotopes:
Examples: \[_1H^1and_1H^2\]
