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.
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 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.
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 energy released due to loss in mass during the processes of nuclear fission and fusion is called nuclear (or atomic) energy.
OR
The energy released when nuclei undergo a nuclear reaction (change in structure, forming new nuclei) is called nuclear energy.
Define binding energy per nucleon.
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`
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.
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.
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.
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 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 average time for which a radioactive nucleus exists before decay is called the mean (average) life τ.
τ = \[\frac {1}{λ}\]
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 process in which a heavy nucleus splits into two lighter nuclei with the release of energy is called nuclear fission.
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.
\[\frac{1}{\lambda}=R\left(\frac{1}{n^2}-\frac{1}{m^2}\right)\]
mvr = \[\frac {nh}{2π}\]
where
\[r_n=a_0\frac{n^2}{Z}\]
\[\rho=\frac{mA}{\frac{4}{3}\pi R^3}\]
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 = [mparent − mproducts]c2
Example form used in fission:
Q = [mU − m1 − m2 − (neutron masses)]c2
Q = [Mass of reactants − Mass of products]c2
Example used in fusion inside the Sun:
Q = [4mp − mα − 2me]c2
The ground state energy of the hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the second excited state is respectively ______
The ground state energy of the hydrogen atom is -13.6 eV. The kinetic and potential energy of the electron in the second excited state is respectively 1.51 eV, -3.02 eV.
Explanation:
For second excited state n = 3
The total energy in the third orbit
`E_3 = (-13.6)/9`eV = -1.51 eV
K.E. = -T.E. = 1.51 eV
P.E. = 2.T.E. = -3.32 eV
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.
