Test: Quantum Mechanical Model of Atom - Chemistry MCQ

The representation of the Schrodinger wave function is given by Ψ_n,l,m. Therefore by comparing Ψ_n,l,m and Ψ_3,1,0 we get that n = 3, l = 1 and m = 0. Here n, l, and m are principal, azimuthal and magnetic quantum numbers respectively. but rememberr they are asking for l , n , m that's why a) option is correct

According to Hund’s rule of maximum multiplicity, the pairing of electrons cannot be started until each of the orbitals is singly occupied. The reason behind this is that the half-filled or fully filled orbitals are much more stable comparatively.

As per the Aufbau’s principle, the orbital or subshell with the lowest energy should be filled first. The ascending order of orbital’s energy is given by 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 4f, 5d, 6p, 7s. So 2s orbital should be filled first.

Total number of nodes include angular and radial nodes. Angular nodes and radial nodes are given by the formula n – l -1 and l respectively. So the total number of nodes are n – l -1 + l = n – 1. For 3d orbit, “n” is 3, so total number nodes is 3 – 1 = 2.

The azimuthal quantum number is given by “l”. When l = 0, 1, 2 and 3, they are s-orbital, p-orbital, d-orbital and f-orbital respectively. The shapes of s-orbital, p-orbital, d-orbital, and f-orbital are Spherical, Dumbbell, Double dumbbell and Complex respectively.

The number of orbitals within an orbit is n2. But as each orbital can accommodate 2 electrons, the number of electrons that can exist with the “n” as the principal quantum number is 2n². So here 2n² = 2(4)² = 2(16) = 32.

The set of quantum number n = 1, l = 2, m = 0, s = 1/2, is not valid because the value of azimuthal quantum number should lie only in between 0 and n-1, where n is principal quantum number. So the above set of quantum numbers is not valid.

The magnetic quantum of an orbital range from -( l – 1) to l – 1. Its symbol is given by m. For 2p orbital, there are 3 magnetic quantum numbers namely -1, 0 and 1. For 2p_z orbital its 0, taken that z is the internuclear axis.

Among the four quantum numbers, the principal quantum number describes the size and energy of the orbit. It is represented by the symbol “n”. For shells, K, L, M, N and O, n is given by 1, 2, 3, 4 and 5.

Yes, no two electrons have the same set of all four quantum numbers. This is explained by Pauli’s exclusive principle. At most electrons can have all 3 quantum numbers the same as they are in the same orbital. But the spin quantum number’s values are different.