s-orbitals: For Is orbital, l = 0 and m = 0, f(θ) = 1/✓2 and g(φ) = 1/✓2π. Therefore, the angular distribution function is equal to 1/✓2π.i.e it is independent of the angle θ and φ. Hence, the probability of finding the electron is independent of the direction from the nucleus. The shape of the s orbital is spherical.

The carbon atom has six electrons. According to Aufbau principle, the electronic configuration is 1s²,2s²,2p² 
It can be represented as below,

In this case, in order to minimise the electron-electron repulsion, the sixth electron enters the unoccupied 2p_y orbital as per Hund's rule. i.e. it does not get paired with the fifth electron already present in the 2P_x orbital

Aufbau's principle does not deal with the filling of electrons in the degenerate orbitals (i.e. orbitals having same energy) such as px, py and pz

To obtain atomic number of an element fill the orbitals in order of their increasing energies up to the given outer orbital configuration
(a) Is²2s², 2p^6, 3s² (Z = 12)
(b) Is² 2S², 2p³ (Z = 7)
(c) Is²2s², 2p⁶, 3s², 3p⁵ (Z = 17)

It states that electron pairing in the degenerate orbitals does not take place until all the available orbitals contains one electron each.

(a) ₁H = 1s¹, H- = 1s2
(b) 11Na = 1s² 2s²,2p⁶,3s¹,Na+ = 1s²2s²2p⁶
(c) 8O = 1s² 2s²,2p⁴,O^2- = 1s²2s²²p⁶
(d) 9F = 1s² 2s²,2p^5,F- =1s²2s2²p⁶

1p is not possible because if n = 1 then l = 0 only and for p, l = 1
2s is possible because if n = 2 then l = 0, 1 and for s, l = 0
2p is possible because if n = 2 then l = 0, 1 and for p, l = 1
3f is not possible because if n = 3 then l = 0, 1 and 2 for f, l = 3.

(a) [He]2s¹ represents ₃Li (lithium)
(b) [Ne]3s²3p³ represents ₁₅P(phosphorus)
(c) [Ar]4s² 3d¹ represents ₂₁SC (scandium).

For 3d-orbital, n = 3, l = 2,m₁ = -2,-1,0,+1,+2

For n = 3, l = 0, 1,2
l= 0,m₁ = 0
l = 1, m₁=-1+0,+1
l = 2,  m₁=-2,-1,0,+1,+2 

(i) n = 3, l = 2
(ii) n = 4, l = 2
(iii) n = 2, l = 2
(iv) n = 4, l = 2
(v) n = 2 , l = 2
(vi) n = 3 , l = 2

(i) is not possible as n ≠ 0
(ii) is possible (Is)
(iii) is not possible because if n = 1, 1 = 0 only (l ≠ 1)
(iv) is possible (2p)
(v) is not possible because if n = 3, 1 = 0 ,1 and 2 (l ≠ 3)
(vi) is possible (3p)

(i) It states that, the lower the value of (n + 1) for an orbital, the lower is its energy. If two orbitals have the same value of (n + 1), the orbital with lower value of n will have the lower energy.
(ii) (a) Principal quantum number : 1s < 2s = 2p < 3s = 3p = 3d <4s = 4p = 4d = 4f < 5s = 5p = 5d = 5f < 6s = 6p = 6d = 6f < 7s
(b) Based on the (n+1) rule: 1s < 2s < 2p < 3s < 3p < 4s <3d <4p <5s <4d < 5p <6s <4f < 5d < 6p < 7s < 5f < 6d.

A = 13, A - Z = 7 (Neutrons)
Then Z= 6
(ie) Atomic number = 6

For 3p-orbital n = 3, l = 1
Number of angular nodes = l = 1
Number of radial nodes = n - l -1 = 3 - 1 - 1 =1

Ferrous and ferric salts: In ferrous salts Fe²⁺,  the configuration is 1s²2s²,2p⁶,3s², 3p⁶, 3d⁶.In ferric salts Fe3⁺ ,the configuration is 1s²2s²,2p⁶,3s², 3p⁶, 3d⁵.
As half-filled 3d⁵ configuration is more stable therefore ferric salts are more stable than ferrous salts.

(i) For a neutral atom,
Number of electrons =number of protons
29 electrons = 29 protons.
(ii) ₂₉z = 1s²,2s²,2p⁶,3s²,3p⁶,3d¹⁰,4s¹
(The element is copper)

The similarities in 1s and 2s-orbitals are as follows :
(i) Both have the spherical shape
(ii) Both have the same angular momentum.
The difference in between them are as follows :
(i) Size of 2s-orbital is larger than that of 1s-orbital.
(ii) Energy of 2s-orbital is greater than that of  1s-orbital.
(iii) 2s-orbital has one node while 1s-orbital has no node.

(i) 2s,2p
(ii) 3p < 3d
(iii) 3s < 4s
(iv) 4d < 5f
This is because lower the value of (n + 1), lower is the energy and if(n + 1) are same, the orbital with lower value of n is of lower energy.

d sub-shell has five orientations. Each orientation can accommodate one electron with spin quantum number +1/2 and another electron with -1/2 Hence number of electrons with s+1/2 in 'd' sub shell is 5.

The number of electrons in an atom of an element is 19.
The electronic configuration is 1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹
The total number of p-orbitals for the element is 2p level- 3 and 3p level- 3. i.e. '6' orbitals.

The K shell or the first energy level does not have p-orbital.

Magnetic quantum number accounts for the orientation of the electron in orbital.

1 value of p-orbital is 1. The possible 'm' values are -1,0 and +1

(i) n= 2 and 1 =0. The orbital is 2s. Its shape is symmetrically spherical.
(ii) n = 2 and 1 = 1. The orbital is 2p. Its shape is dumbbell.

The region within the orbital where the probability of finding the electron is zero is called a node

Maximum number of electrons in any shell is given by the expression 2n² where n is the principal quantum number,

(i) The energy of photon is sufficient to disturb a sub-atomic particle so that there is uncertainty in the measurement of position and momentum of the sub-atomic particle.
(ii) However, the energy is insufficient to disturb a macroscopic object.

From de Broglie equation, wavelength \(\lambda =\frac { h }{ mv } \)
For same wavelength with two different particles, (ie) electron and proton m₁v₁ = m₂v₂ (h is constant) Lesser the mass of the particle, greater will be the velocity.
Hence electron will have higher velocity

Quantum numbers are a set of four numbers which are used to specify the position, energy, shape, size, angular momentum, magnetic properties spin and orientation of an electron in an atom.