Orbitals are region or space wher.e there is maximum probability of finding electrons. Qualitatively, these orbitals can be distinguished by their size, shape and orientation. An orbital of small size means there is more chance of finding the electron near the nucleus. Shape and orientation means the direction in which probability of finding electron is maximum. Atomic orbitals can be distinguished by quantum numbers. Each orbital is designated by three quantum numbers n, I and m₁ (magnetic quantum number) which define energy, shape and orientation but these are not sufficient to explain spectra of multi-electrons atoms. Spin quantum number (m_s ) determines the spin of electron. Spin angular momentum of electron has two orientations relative to chosen axis which are distinguished by spin quantum numbers m_s which can take values +1/2 and -1/2.

(a) How many orbitals are associated with n = 3?
(b) Describe the orbitals represented by (i) n = 2, l = 1 (ii) n = 4, l = 0.
(c) How many electron are possible in an orbital? Why?
(d) What is shape of 's' and 'p' orbitals?
(e) Name two d-orbitals which are on axis.

The plots of (a) orbital wave function \(\Psi\)(r) and (b) the variation of probability density\(\Psi\) ²(r) as function of distance'r' of the electron from the nucleus for Is and 2s orbitals are shown in the figure. Answer the questions as follows based on graph and related studied concepts.


(a) What is meant by\(\Psi\)?
(b) What is meant by \(\Psi\)²?
(c) What happens to probability density in Is orbital?
(d) What happens to \(\Psi\) ² in '2s' orbital?
(e) What are nodes?
(f) How many nodes are 1s, 2s, 3s orbitals?
(g) What are angular nodes?
(h) How many radial and angular nodes are there in 3d orbital?

Bohr's model explained electrons can revolve only in certain permitted orbits whose angular momentum is integral multiple of h/2\(\pi\), associated with fixed amount of energy. Bohr theory could successfully explain stability of atoms and spectrum of unielectron species. Hydrogen spectrum consist of Lyman, Balmer, Paschen, Brackett and Pfund series. Bohr's theory could not explain spectrum of multi-electron species, Stark effect, Zeeman effect, dual nature of matter, de Broglie equation and Heisenberg uncertainty principle which lead to orbital concept. Electrons were filled in orbitals according to Autbau's principle, Hund's Rule and Pauli's exclusion principle. Each electron is identified by four quantum numbers n, I, m_l and m_s out which n, I, m_l were derived from Schrodinger's wave equation. Half filled and completely filled orbitals are more stable due to exchange energy and symmetrical distribution of electrons.
(a) Heat treatment of muscular pain involves radiation of wavelength 900 nm which spectral line of H-atom is suitable for this purpose.
(b) Arrange 4d, 3d, 4p and 3p in increasing order of energy.
(c) What is name of spectrum of radiation emitted by substance that has absorbed radiation?
(d) What rules out the probability of existence of definite path of electrons?
(e) State de Broglie equation.
(f) The angular momentum of d-orbital is equal to?
(g) State Pauli exclusion principle.