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NEET Physics Atoms and Nuclei

Atoms and Nuclei PDF Notes, Important Questions and Synopsis

SYNOPSIS
  • Thomson’s model of an atom:
    An atom consists of positively charged matter in which the negatively charged electrons are uniformly embedded like plums in a pudding. This model could not explain the scattering of α-particles through thin foils and was hence discarded.

  • Rutherford’s model of an atom:
    Geiger and Marsden in their experiment on scattering of a-particles found that most of the a-particles passed undeviated through thin foils, but some of them were scattered through very large angles. 

    From the results of these experiments, Rutherford proposed the following model of an atom:
    • An atom consists of a small and massive central core in which the entire positive charge and almost the whole mass of the atom are concentrated. This core is called the nucleus.
    • The nucleus occupies a very small space as compared to the size of the atom.
    • The atom is surrounded by a suitable number of electrons so that their total negative charge is equal to the total positive charge on the nucleus and the atom as a whole is electrically neutral.
    • The electrons revolve around the nucleus in various orbits just as planets revolve around the sun. The centripetal force required for their revolution is provided by the electrostatic attraction between the electrons and the nucleus. This model could not explain the instability of the atom, because according to the classical electromagnetic theory, the electron revolving around the nucleus must continuously radiate energy in the form of electromagnetic radiation, and hence, it should fall into the nucleus.

 

  • Distance of closest approach:
    When an a-particle of mass m and velocity v move directly towards a nucleus of atomic number Z, its initial energy Ei which is just the kinetic energy K gets completely converted to potential energy U at the stopping point. This stopping point happens to be at a distance of the closest approach d from the nucleus
    begin mathsize 12px style straight E equals 1 half mv squared equals fraction numerator 1 over denominator 4 πε subscript straight o end fraction fraction numerator 2 eZe over denominator straight d end fraction equals fraction numerator 2 Ze squared over denominator 4 πε subscript straight o straight d end fraction end style
    Hence, begin mathsize 12px style straight d equals fraction numerator 2 Ze squared over denominator 4 πε subscript straight o straight K end fraction end stylebegin mathsize 12px style straight d equals fraction numerator 2 Ze squared over denominator 4 πε subscript straight o straight K end fraction end style

  • Bohr’s model for the hydrogen atom:
    Basic postulates:
  1. Nuclear concept: An atom consists of a small massive centre 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.

  2. Quantum condition: Of all the possible circular orbits allowed by the classical theory, the electrons are permitted to circulate only in such orbits in which the angular momentum of an electron is an integral multiple of h/2Π, h being Planck’s constant.
    begin mathsize 12px style straight L equals mvr equals fraction numerator nh over denominator 2 straight pi end fraction comma straight n equals 1 comma 2 comma 3 .... end style
    where n is called the principal quantum number.

  3. Stationary orbits: While revolving in the permissible orbits, an electron does not radiate energy. These non-radiating orbits are called stationary orbits.


  4. Frequency condition: An atom can emit or absorb radiation in the form of discrete energy photons only when an electron jumps from a higher orbit to a lower orbit or from a lower orbit to a higher orbit. If E1 and E2 are the energies associated with these permitted orbits, then the frequency ν of the emitted absorbed radiation is given by hυ = E2 − E1
  • Radius of the orbit of an electron in the hydrogen atom is 
     begin mathsize 12px style straight r equals fraction numerator straight e squared over denominator 4 πε subscript straight o mv squared end fraction end style
    begin mathsize 12px style straight r proportional to straight n squared over straight z end style

  • Potential Energy U
    begin mathsize 12px style straight U equals negative fraction numerator Ze squared over denominator 4 πε subscript straight o straight r end fraction end style
  • Total Energy E of the electron in the electron in the hydrogen atom:
    E = K + Ubegin mathsize 12px style equals negative fraction numerator Ze squared over denominator 8 πε subscript straight o straight r end fraction end style
  • Speed of an electron in the nth orbit is given by
    begin mathsize 12px style straight v equals fraction numerator 2 πke squared over denominator nh end fraction equals straight alpha straight c over straight n equals 1 over 137. straight c over straight n end style
    where begin mathsize 12px style straight alpha equals fraction numerator 2 πke squared over denominator ch end fraction end styleis the fine structure constant. 
    begin mathsize 12px style straight v proportional to straight Z over straight n end style
  • Energy of an electron in the nth orbit is given by
    Error converting from MathML to accessible text.

  • Spectral series of the hydrogen atom:
    Whenever an electron in the hydrogen atom makes a transition from a higher energy level n2 to a lower energy level n1, the difference of energy appears in the form of a photon of frequency v given by
    begin mathsize 12px style straight nu equals fraction numerator 2 straight pi squared mk squared straight e squared over denominator straight h squared end fraction open square brackets fraction numerator 1 over denominator straight n subscript 1 superscript 2 end fraction minus fraction numerator 1 over denominator straight n subscript 2 superscript 2 end fraction close square brackets end style
    Different spectral series of the hydrogen atom are as follows
  1. Lyman series: n2 = 2, 3, 4,… and n1 = 1; lies in the ultraviolet region.
  2. Balmer series: n2 = 3, 4, 5,… and n1 = 2; lies in the visible region.
  3. Paschen series: n2 = 4, 5, 6,… and n1 = 3; lies in the infrared region.
  4. Brackett series: n2 = 5, 6, 7,… and n1 = 4; lies in the infrared region.
  5. Pfund series: n2 = 6, 7, 8,… and n1 = 5; lies in the infrared region.
  • Excitation energy:
    Energy required by an electron of an atom to jump from its ground state to any one of its excited states

  • Ionisation energy
    Energy required to remove an electron from an atom, i.e. the energy required to take an electron from its ground state to the outermost orbit (n = ∞).

  • Excitation potential:
    It is that accelerating potential which gives sufficient energy to a bombarding electron so as to excite the target atom by raising one of its electrons from an inner orbit to an outer orbit.

  • Ionisation potential: 
    It is the accelerating potential which gives a bombarding electron sufficient energy to move to an outer orbit.

  • Maser:
    Maser stands for ‘Microwaves Amplification by Stimulated Emission of Radiation’. It is a device for producing a highly intense, monochromatic coherent and collimated beam of microwaves.

  • Laser:
    Laser stands for ‘Light Amplification by Stimulated Emission of Radiation’. It is a device used to produce a highly intense strong monochromatic coherent and collimated beam of light.

  • X-Rays:
    X-rays are electromagnetic radiations of very short wavelength and high energy which are emitted when fast-moving electrons or cathode rays strike a target of high atomic mass. X-rays are of two types—characteristic X-rays and continuous X-rays.
    Applications of X-rays:
    X-rays are used in radio therapy, medicine and surgery.

  • Moseley's law:
    begin mathsize 12px style square root of straight v equals straight a open parentheses straight Z minus straight b close parentheses end style
    where
    V = frequency
    a and b = positive constants
    Z = atomic number

  • Atomic number: Number of protons in the nucleus. It is denoted by Z. 

  • Nuclear mass: Total mass of the protons and neutrons present in a nucleus.

  • Isotopes: Atoms of an element which have the same atomic number but different mass number. Isotopes have similar chemical properties but different physical properties.

  • Isobars: Atoms with the same mass number but different atomic number.

  • Isotones: Nuclides with the same number of neutrons.

  • Atomic mass unit: It is begin mathsize 12px style 1 over 12 end styleth of the actual mass of a carbon atom of isotope 6C12
    It is denoted by amu or just by u.
    1 amu = 1.660565 × 10−27 kg
    The energy equivalence of 1 amu is
    1 amu = 931 MeV

  • Size of the nucleus: It is found that a nucleus of mass number A has a radius
    R = R0A1/3
    where R0 = 1.2 × 10−15 m
    This implies that the volume of the nucleus, which is proportional to R3, is proportional to A.
    The density of a nucleus is constant and independent of A for all nuclei, and the density of nuclear matter is approximately 2.3 × 1017 kg m−3 which is very large as compared to ordinary matter, say water, which is 103 kg m−3.

  • Mass defect: The difference between the rest mass of a nucleus and the sum of the rest masses of its constituent nucleons. It is given by
    Δm = [Zmp + (A − Z)mn] – m

  • Binding energy: Energy required to break up a nucleus into its constituent protons and neutrons and to separate them to such a large distance that they may not interact with each other.
    It may also be defined as the surplus energy which the nucleus gives up by virtue of their attractions which they become bound together to form a nucleus. 
    Binding energy of a nucleus zXA is given by 
    BE = [Zmp + (A − Z)mn – m]c2 

  • Binding energy per nucleon: It is the average energy required to extract one nucleon from the nucleus. It is obtained by dividing the binding energy of a nucleus by its mass number.
    begin mathsize 12px style straight B with bar on top equals fraction numerator straight B. straight E over denominator straight A end fraction equals fraction numerator left square bracket Zm subscript straight p plus left parenthesis straight A minus straight Z right parenthesis straight m subscript straight n minus straight m right square bracket text   end text straight c squared over denominator straight A end fraction end style

  • Nuclear forces: These are the strong attractive forces which hold protons and neutrons together in a tiny nucleus. These are short-range forces which operate over a very short distance of about 2–3 fm of separation between any two nucleons. The nuclear force does not depend on the charge of the nucleon. 

  • Nuclear density: Density of the nucleus is independent of its size and is given by
    begin mathsize 12px style straight rho subscript straight v equals fraction numerator Nuc text   end text lear text   end text mass over denominator Nuc text   end text lear text   end text volume end fraction end style
    Error converting from MathML to accessible text.
  • Radioactivity: The phenomenon of spontaneous disintegration of the nucleus of an atom with the emission of one or more radiations such as α-particles, β-particles or γ-rays. Substances which spontaneously emit penetrating radiation are called radioactive substances.
     
  • Radioactivity displacement law:
  1. When a radioactive nucleus emits an α-particle, the atomic number decreases by 2 and the mass number decreases by 
  2. When a radioactive nucleus emits a β-particle, the atomic number increases by 1 but the mass number remains the same.
  3. Emission of a γ-particle does not change the mass number or the atomic number of the radioactive nucleus. γ-particle emission by a radioactive nucleus lowers its energy state.
  • Alpha decay: The process of emission of an α-particle from a radioactive nucleus. It may be represented asbegin mathsize 12px style straight X presubscript straight z presuperscript straight A rightwards arrow straight Y presubscript straight z minus 2 end presubscript presuperscript straight A minus 4 end presuperscript plus He presubscript 2 presuperscript 4 plus straight Q end style

  • Beta decay: The process of emission of an electron from a radioactive nucleus. It may be represented asbegin mathsize 12px style straight X presubscript straight z presuperscript straight A rightwards arrow straight Y presubscript straight z plus 1 end presubscript presuperscript straight A plus straight e presubscript negative 1 end presubscript presuperscript 0 plus straight nu with bar on top end style

  • Gamma decay: The process of emission of a γ-ray photon during the radioactive disintegration of a nucleus. It can be represented as
     begin mathsize 12px style table attributes columnalign left end attributes row cell straight X presubscript straight z presuperscript straight A space space space space space space space space space space space space rightwards arrow space space space space space space space space space space space space space straight X presubscript straight z presuperscript straight A plus straight gamma end cell row cell left parenthesis Excited text   end text state right parenthesis left parenthesis Ground text   end text state right parenthesis end cell end table end style

  • Radioactive decay law: Number of nuclei undergoing decay per unit time is proportional to the number of undecayed radioactive nuclei present at that instant. It may be written as 
    N (t) = N (0) et, 
    where N (0) is the number of nuclei at t = 0 and λ is the disintegration constant.


  • Decay or disintegration constant: Reciprocal or the time interval in which the number of active nuclei in a given radioactive sample reduces to 36.8% begin mathsize 12px style open parentheses or 1 over straight e times close parentheses end style of its initial value.

  • Half-life: Time in which one-half of the nuclei of a radioactive substance will disintegrate. It is inversely proportional to the decay constant of the radioactive substance.
    Error converting from MathML to accessible text.

  • Mean life: Ratio of the combined age of all the atoms and the total number of atoms in a radioactive sample. It is given by
    Error converting from MathML to accessible text.

  • Nuclear reaction: A reaction which involves the change of stable nuclei of one element into the nucleus of another element. 

  • Nuclear fission: A process in which a heavy nucleus when excited gets split into two smaller nuclei of nearly comparable masses. 
    Example: begin mathsize 12px style straight U presubscript 92 presuperscript 235 plus straight n presubscript 0 presuperscript 1 rightwards arrow Ba presubscript 56 presuperscript 141 plus Kr presubscript 36 presuperscript 92 plus 3 straight n presubscript 0 presuperscript 1 plus straight Q end style

  • Nuclear reactor: A device in which a nuclear chain reaction is initiated, maintained and controlled.

  • Nuclear fusion: A process of fusion of two smaller nuclei into a heavier nucleus with the liberation of a large amount of energy.