(a) How many subshells are associated with$\mathrm{n}=4$ ? (b) How many electrons will be present in the subshells having ${\mathrm{m}}_{\mathrm{s}}$ value of $-1/2$ for $\mathrm{n}=4$ ?

(i) Atom is made up of electrons, protons and neutrons called fundamental particles.

(ii) Electron was discovered by J. J. Thomson from study of cathode rays.

(iii) Mass of electron $=$ 9.11 × 10-31 kg = 11837th of that of $\mathrm{H}$-atom.

(iv) Charge on electron = 1.602 × 10-19 coulomb.

(v) $\frac{\mathrm{e}}{{\mathrm{m}}_{\mathrm{e}}}=1.758820{ \times 10}^{\mathrm{11}} \mathrm{C} {\mathrm{Kg}}^{-1}$

(vi) Proton was discovered by Goldstein from study of anode rays using a perforated cathode in the discharge tube.

(vii) Neutron was discovered by Chadwick by bombarding $\mathrm{Be}$ or $\mathrm{B}$ atoms with α-rays.

2. Atomic number and mass number:

(i) Atomic number $\left(\mathrm{Z}\right) =$ number of protons in the nucleus of an atom $=$ number of electrons in a neutral atom

(ii) Mass number $\left(\mathrm{A}\right) =$ number of protons $\left(\mathrm{Z}\right) +$ number of neutrons $\left(\mathrm{n}\right)$

(iii) We represent atomic number $\left(\mathrm{Z}\right)$  and mass number $\left(\mathrm{A}\right)$  along with the element $\left(\mathrm{X}\right)$  as ZAX.

3. Isobars and Isotopes:

(i) Atoms of the same element having same atomic number, but different mass numbers are called isotopes.

(ii) Atoms of different elements having different atomic numbers but same mass number are called isobars.

4. Isoelectronic species:

Species (atoms or ions) containing same number of electrons are called isoelectronic species.

5. Wave Nature of Electromagnetic Radiation:

(i) $\mathrm{c}=\mathrm{\nu }\times \mathrm{\lambda }$

(ii) Wave number $\left(\stackrel{-}{\mathrm{v}}\right)$. It is equal to reciprocal of wavelength $\left(\stackrel{-}{\mathrm{v}}=\frac{1}{\mathrm{\lambda }}\right)$

6. Planck's Quantum Theory:

Energy of one photon $=\mathrm{h\nu }=\frac{\mathrm{hc}}{\mathrm{\lambda }}$

7. Photoelectric effect:

(i) K.E. of ejected electron, $\frac{1}{2}{\mathrm{mv}}^2 = \mathrm{hv} - {\mathrm{hv}}_0$

(ii) $\mathrm{1 }\mathrm{eV} {=1·602\times 10}^{-\mathrm{19}}\mathrm{J}$

8. Hydrogen spectrum:

9. Bohr’s model of atom:

(i) Rydberg formula: $\stackrel{-}{v}=\mathrm{R}\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right){\mathrm{Z}}^2$

R = Rydberg constant $= 109677 {\mathrm{cm}}^{-1} \mathrm{or} 1·097 \times 107 {\mathrm{m}}^{-1}$

(ii) Frequency of radiation absorbed or emitted during transition: $v=\frac{\mathrm{\Delta E}}{\mathrm{h}}\mathrm{=}\frac{{\mathrm{E}}_{\mathrm{2}}-{\mathrm{E}}_{\mathrm{1}}}{\mathrm{h}}$

(iii) Quantization of angular momentum: $\mathrm{mvr}=\mathrm{n}\frac{h}{2\pi }$

(iv) Energy of stationary states: ${\mathrm{E}}_{\mathrm{n}}\mathrm{=}-\frac{21.8{\times 10}^{-\mathrm{19}}}{{\mathrm{n}}^{\mathrm{2}}}{\mathrm{Z}}^{\mathrm{2}}\hspace{0.17em}\mathrm{J}\hspace{0.17em}{\mathrm{atom}}^{-1}$

(v) Radii of the stationary orbits: ${\mathrm{r}}_{\mathrm{n}}=52.9\times \left(\frac{{\mathrm{n}}^{\mathrm{2}}}{\mathrm{Z}}\right)\mathrm{pm}$

(vi) Energy gap between two orbits: $\mathrm{\Delta E}={\mathrm{R}}_{\mathrm{H}}\left(\frac{\mathrm{1}}{{\mathrm{n}}_{\mathrm{i}}^{\mathrm{2}}}-\frac{\mathrm{1}}{{\mathrm{n}}_{\mathrm{f}}^{\mathrm{2}}}\right)$

Where, ${\mathrm{n}}_{\mathrm{i}}$ and ${\mathrm{n}}_{\mathrm{f}}$ are initial orbit and final orbit respectively.

10. de Broglie relation is$\mathrm{\lambda } = \mathrm{h}/\mathrm{mv} = \mathrm{h}/\mathrm{p}$ where $\mathrm{\lambda }$ is wavelength, $\mathrm{m}$ is mass, $\mathrm{\nu }$ is velocity and $\mathrm{p}$ is momentum of the material particle.

11. Heisenberg's uncertainty principle:

$\mathrm{\Delta x}.\mathrm{\Delta p}>\frac{h}{4\mathrm{\pi }}\text{ or }\mathrm{m\Delta x}.\mathrm{\Delta v}\ge \frac{\mathrm{h}}{4\mathrm{\pi }}\text{ or }\mathrm{\Delta x}.\mathrm{\Delta v}\ge \frac{\mathrm{h}}{4\mathrm{\pi m}}$

12. Quantum numbers: To find the exact position of electron four quantum numbers are required.

(i) Principal quantum number

(ii) Azimuthal quantum number

(iii) Magnetic quantum number

(iv) Spin quantum number

13. Filling of Orbitals in Atom:

(i) Aufbau principle: Electrons in the ground state atom are filled in the orbitals in an increasing order of energy.

(ii) Pauli exclusion principle: No two electrons in an atom can have the same set of four quantum numbers.

(iii) Hund’s rule of maximum multiplicity: Pairing of electrons in the orbitals belonging to the same subshell does not occur unless each orbital belonging to that subshell has got one electron each.

14. Electronic configuration:

(i) Electronic configuration of an atom is the distribution of its electrons in orbitals.

(ii) Electronic configurations of $\mathrm{Cu}$ and $\mathrm{Cr}$

Copper: $1{\mathrm{s}}^2 2{\mathrm{s}}^2 2{\mathrm{p}}^6 3{\mathrm{s}}^2 3{\mathrm{p}}^6 4{\mathrm{s}}^1 3{\mathrm{d}}^{10}$

Chromium: $1{\mathrm{s}}^2 2{\mathrm{s}}^2 2{\mathrm{p}}^6 3{\mathrm{s}}^2 3{\mathrm{p}}^6 4{\mathrm{s}}^1 3{\mathrm{d}}^5$