NEET 2021 Short Notes: Atoms and Nuclei

Atoms and Nuclei

Rutherford Atomic Model

Rutherford experiments on the scattering of α-particles by thin gold foil

In this experiment, α-particles are emitted by some radioactive material (polonium), kept inside a thick lead box. A very fine beam of α-particles passes through a small hole in the lead screen. This well-collimated beam is then allowed to fall on a thin gold foil. While passing through the gold foil, α-particles are scattered through different angles. A zinc sulfide screen was placed out the other side of the gold foil. This screen was movable, so as to receive the α-particles, scattered from the gold foil at angles varying from 0 to 180°.

According to the experiment, electrons revolve around the nucleus in circular orbits. Atom is positive charge, instead of being uniformly distributed throughout a sphere of atomic dimension is concentrated in a very small volume at it center. This central core is called nucleus, is surrounded by clouds of the electron makes. The entire atom electrically neutral.

Bohr's Atomic Model

According to the Bohr's Atomic Model electron is revolving around the nucleus in a circular orbit. Bohr's atomic model is similar to the Sun-Planet system.

Bohr incorporated the following new ideas now regarded as postulates of Bohr's theory.

1. The centripetal force required for an encircling electron is provided by the electrostatic attraction between the nucleus and the electron

2. Electrons can revolve only in those orbits in which angular momentum of the electron about nucleus is an integral multiple of h/2π.

mvr = nh/2π

where n = Principal quantum number of the orbit in which electron is revolving.

3. Electrons in an atom can revolve only in discrete circular orbits called stationary energy levels (shells). An electron in a shell is characterized by definite energy, angular momentum, and orbit number. While in any of these orbits, an electron does not radiate energy although it is accelerated.

4. Electrons in outer orbits have greater energy than those in inner orbits. The orbiting electron emits energy when it jumps from an outer orbit (higher energy states) to an inner orbit (lower energy states) and also absorbs energy when it jumps from an inner orbit to an outer orbit. E_n – E_m = hv_n,m

where, E_n = Outer energy state, E_m = Inner energy state and v_n,m = Frequency of radiation

The energy absorbed or released is always in the form of electromagnetic radiations.

The velocity of the electron in n^th orbit:

The radius of the n^th orbit:

The total energy of the electron in n^th orbit:

The time period of revolution of the electron in n^th orbit:

The frequency of revolution in n^th orbit:

Spectral Series of hydrogen atom

In an atom, the energy of the outer orbit is greater than the energy of the inner ones. When the Hydrogen atom is subjected to external energy, the electron jumps from the lower energy state to excited state. The electron return to its ground state in about 10^–8 sec. The excess of energy is now radiated in the form of radiations of a different wavelength. The different wavelength constitutes spectral series. Which are characteristic of atom emitting, then the wavelength of different members of series can be found from the following relations.

Lyman Series: The series consists of the wavelength which is emitted when the electron jumps from an outer orbit to the first orbit. i.e. the electron is jumps to K orbit give rise to Lyman series.

Balmer Series: This series consists of the wavelength which is emitted when the electron jumps from an outer orbit to the second orbit. i.e., the electronic jumps to L orbit give rise to Balmer series.

Paschen Series: This series consists of all wavelength are emitted when an electron jumps from an outer orbit to the third orbit i.e., the electron jumps to M orbit give rise to paschen series.

Bracket Series: This series is consist of all wavelength which is emitted when an electron jumps from an outer orbit to the fourth orbit i.e., the electron jumps to N orbit give rise to Brackett series.

Pfund series: The series consists of all wavelength which is emitted when an electron jumps from an outer orbit to the fifth orbit i.e., the electron jumps to O orbit give rise to Pfund series.

Atomic Nucleus

The atomic nucleus consists of two types of elementary particles, neutrons and protons. These particles is known as nucleons.

Proton- The proton has charge +e (1.6 × 10^-19 C) and mass m_p (1.6726 × 10^-27 kg). The mass of the proton is much larger than the mass of the electron.

Neutron- The neutron is an electrically neutral particle and mass of the neutron is m_n = 1.6749 × 10^-27 kg.

Mass Defect- The difference between the total mass of the nucleons and mass of the nucleus is called the mass defect of the nucleus

Binding Energy- The rest mass of the nucleus is smaller than the sum of the rest masses of nucleons constituting it. This is due to when nucleons combine to form a nucleus, some energy (binding energy) is liberated. The binding energy is equal to the work that must be done to split the nucleus into the particles constituting it.

Binding Energy per Nucleon- Binding energy per nucleon is used to determine the stability of a nucleus.

Nuclear fission- Nuclear fission is the process when a heavy nucleus is split into two or more lighter nuclei. In this process, certain mass disappears which is obtained in the form of energy (an enormous amount)

Nuclear Fusion- Nuclear fusion is the process in which two or more lighter nuclei to form a single heavy nucleus.

The product (C) is more stable then reactants (A and B) & m_c < (m_a + m_b)

mass defect is,

Energy released is

The total binding energy and binding energy per nucleon C both are more than of A and B

X-Rays

X-rays are the form of electromagnetic radiation. X-rays are produced by bombarding high-speed electrons on a target of high atomic weight and high melting point.

Continuous spectrum of X-ray- When a high-speed electron collides from the atom of the target and passes close to the nucleus. There is coulomb attractive force due to this electron is deaccelerated. The loss of energy during deacceleration is emitted in the form of X-rays and these X-rays

Characteristic Spectrum of X-ray

When the target of the X-ray tube is collied by energetic electron it emits two type of X-ray radiation. One of them has a continuous spectrum whose wavelength depend on applied potential while other consists of spectral lines whose wavelength depend on the nature of the target. The radiation forming the line spectrum is called characteristic X-rays.

Diffraction of X-ray

Diffraction of X-ray is possible by crystals because the interatomic spacing in a crystal lattice is the order of the wavelength of X-rays.

according to Bragg's law for constructive interference in diffraction of X-ray, 2d sinθ = nλ

where, d = spacing of crystal plane or lattice constant, θ = Bragg's angle or glancing angle, ϕ = Diffracting angle and n = 1, 2, 3 …………..

Properties of X-Ray

1. X-ray always travel with the velocity of light in a straight line.

2. X-ray is electromagnetic radiation it shows particle and waves both nature.

3. In reflection, diffraction, interference and refraction X-ray shows wave nature while in photoelectric effect it shows particle nature.

4. There is no charge on X-ray thus these are not deflected by the electric field and magnetic field.

5. X-ray affects the photographic plate

6. When X-ray incidents on the surface of substance it exerts force and pressure and transfer energy and momentum

Moseley's Law

Moseley studied the characteristic X-rays, and find that when the square root of the frequencies of the characteristic x-rays from the elements is plotted against the atomic number, a straight line is obtained.

Radioactivity

Radioactivity is the phenomenon in which radioactive nuclide spontaneously disintegrate or decay into other stable nuclides. There are three types of radioactive decays.

(i) α-decay: In this decay, the alpha particle is emitted from the radioactive nuclide. The emission of one α-particle reduces the mass number by 4 units and atomic number by 2 units. If parent and daughter nuclei are represented by symbols X and Y respectively then.

(ii) β-decay: In this decay, the beta particle is emitted from the radioactive nuclide. Beta particles are the fast-moving electrons coming from the nucleus of a radioactive substance. This doesn't mean that the nucleus contains electron. When a nucleus emits a beta particle, one of its neutrons breaks into a proton, an electron (i.e., β-particle) and an antineutrino

where n is a neutron, p is the proton, and e is β-particle

Thus emission of a beta particle is caused by the decay of a neutron into a proton. The daughter nucleus thus has an atomic number greater than one (due to one new proton in the nucleus) but the same mass number as that of parent nucleus.

Therefore, representing the parent and daughter nucleus by symbols X and Y respectively, we have

(iii) γ-decay: In this decay, the gamma rays is emitted from the radioactive nuclide. When parent atoms emit gamma rays, no charge is involved as these are neutral rays. Thus there is no effect on the atomic number and mass number of the parent nucleus. However, the emission of γ-rays represents energy. Hence the emission of these rays changes the nucleus from an excited (high energy) state to a less excited (lower energy) state.

Laws of Radioactive Decay

The radioactive decay is a spontaneous process with the emission of α, β and γ rays. It is not influenced by external conditions such as temperature, pressure, electric and magnetic fields.

The rate of disintegration is directly proportional to the number of radioactive atoms present at that time i.e., the rate of decay ∝ number of nuclei.

Rate of decay = λ (number of nuclei) i.e. dN/dt = – λN

where λ is called the decay constant. This equation may be expressed in the form dN/N = –λdt.

where N₀ is the number of parent nuclei at t = 0.

The equation of radioactive decay is , where

Activity- The activity of a radioactive sample is the number of disintegrations per second that occur. The number of disintegrations per second that occur in a sample is proportional to the number of radioactive nuclei present.

Half life time (T_h): It is the time during which the number of active nuclei reduce to half of the initial value.

If at t = 0 no. of active nuclei N₀ then at t = T_h number of active nuclei will be N₀/2

From decay equation N = N₀e^–λt

Mean or Average Life (T_a): It is the average of age of all active nuclei.

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