Solution-Class-11-Science-Chemistry-Chapter-4-Structure of Atom-Maharashtra Board

(b) decreasing

(a)  6.626 × 10^-34Js

(b)  dumb bell

(a)  Pauli’s exclusion principle

(b) size of the orbital

Atomic number = 11 − 6 = 5

 Element is \(_{5}^{11}\text{B}\)

Since hydrogen atom has one electron it shows the simplest emission spectrum.

Heisenberg uncertainty principle : This principle states that it is not possible to determine simultaneously the position and momentum of a moving microscopic particle like electron with absolute certainty.

Quantum numbers are as follows :

• Principal quantum number denoted by n.
• Azimuthal quantum number denoted by l.
• Magnetic quantum number denoted by m_l
• Spin quantum number denoted by m_s.

∴Isoelectronic species : (i) Ne   O²⁻  Na⁺  (ii) Ar    Cl⁻  K⁺

Isotones : The atoms of different elements having same number of neutrons in their nuclei are called isotones.

Isoelectronic species : Atoms and ions having the same number of electrons are isoelectronic species.

Example  :

Consider K⁺ formed by removal of one electron from K atom. Which has 19 electrons (Z = 19). Therefore K⁺ has 18 electrons.

Species such as Ar, Ca²⁺ containing 18 electrons are isoelectronic with K⁺ .

Electronic configuration of all these species with 18 electrons is 1s², 2s², 2p⁶, 3s², 3p⁶.

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

The electronic configuration can be written by applying the aufbau principle.

There are two methods of representing electronic configuration:

(a) Orbital notation: ns^a np^b nd^c..........

For example for boron atom ₅B 1s², 2s², 2p¹.

(b) Orbital diagram:

The capacity of an orbital to accommodate electrons is decided by Pauli exclusion  principle.

Statement of Pauli’s principle : No two electrons in an atom can have all the four quantum numbers, (n, l, m and s) same.

OR

Only two electrons may exist in the given orbital having three quantum numbers same but fourth quantum number being different with opposite spins.

This principle describes the capacity of a sub-shell or orbital to accommodate maximum number of electrons.

Consider helium atom, which has two electrons. The four quantum numbers of two electrons in He atom will be,

Hence 1s orbital can accommodate two electrons.

This principle is illustrated with helium atom He (Z = 2). Its electronic configuration is 1s² as

Statement of Hund’s rule of maximum multiplicty : It states that pairing of electrons in the orbitals belonging to the same subshell does not occur unless each orbital belonging to that subshell has accommodated one electron each.

• Consider filling of p-subshell which has three degenerated orbitals namely

After filling three electrons, one in each with same spins, the next electrons enter with pairing

It observed that half filled and completely filled set of degenerate orbitals have extra stability.

Rutherford’s atomic model has following drawbacks :

• According to the classical electromagnetic theory, a revolving charged particle like electron should emit radiation and lose energy. Due to this, electron should come closer to the nucleus by following a spiral path and finally fall into the nucleus, giving unstable atom. But in reality atoms are stable.
• The orbital motion is an accelerated motion accompanied by continuous change in the velocity of electron due to changing direction.
• Orbital motion of an electron dos not explain the change in energy and hence atomic spectrum.
• The electron would follow a spiral path and fall into the nucleus.
• This model does not explain the distribution of electrons around the nucleus and their energies.

Postulates of Bohr atomic theory

Bohr’s model of hydrogen atom is based on the following postulates.

(i) The electron in the hydrogen atom can move around the nucleus in certain permitted circular orbits arranged concentrically in increasing order of energy.

(ii) The energy of an electron in the orbit does not change with time. Hence orbits are called stationary orbits. On absorption of required energy electron moves from lower orbit to higher orbit.

The transition from higher energy orbit to lower energy orbit is accompanied by emission of energy in the form of electromagnetic radiation.

(iii) The frequency ν of radiation absorbed or emitted on transition between two stationary orbits differing by energy ΔE is given by,

ν = ΔE/h = E₂ − E₁

where E₁ and E₂ are the energies of the lower and higher energy states respectively. Above equation represents Bohr’s frequency rule.

(iv) An electron can occupy only those orbits in which its angular momentum is integral (n) multiple of h/2π

Angular momentum = \(\frac{nh}{2π}\)

Demerits of Bohr model

• Bohr’s atomic model failed to account for finer details of the hydrogen atom spectrum observed in sophisticated spectroscope experiments.
• Bohr model was unable to explain the spectrum of atoms other than hydrogen.
• Bohr theory could not explain the splitting of spectral lines in the presence of a magnetic field (Zeeman effect) or electric field (Stark effect).
• Bohr theory failed to explain the ability of atoms to form molecules by chemical bonds.

Aufbau is a German word which means building up. This principle explains the sequence of filling up of orbitals with electrons.

Aufbau principle : It states that in the ground state of an atom, the orbitals are filled with electrons in order of the increasing energies.

The orbitals are filled in order of increasing value of (n + l). For example, 4s-orbital

(n + l = 4 + 0 = 4) is filled prior to 3d-orbital (n + l = 3 + 2 = 5).

Among two orbitals having same (n + l) value, that orbital with lower value of n will be filled first. For example, 3d-orbital (n + l = 3 + 2 = 5) is filled prior to 4p-orbital (n + l = 4 + 1 = 5).

The increasing order of energy of different orbitals is as follows :

1s<2s<2p<3s<3p<4sz<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d

Anomalous behaviour of copper :

Copper (₂₉Cu) has electronic configuration.

₂₉Cu (Expected) : 1s², 2s², 2p⁶, 3s², 3p⁶, 3d⁹, 4s²

       (Observed) : 1s², 2s², 2p⁶, 3s², 3p⁶, 3d¹⁰, 4s¹

Explanation :

• The energy difference between the 3d- and 4s-orbitals is very low.
• d-orbitals being degenerate, they acquire more stability when they are completely filled.
• Therefore, there arises a transfer of one electron from 4s-orbital to 3d-orbital in Cu giving completely filled more stable d-orbital.
• Hence, the configuration of Cu is [Ar] 3d¹⁰ 4s¹ and not [Ar] 3d⁹ 4s².
• This shows anomalous behaviour of copper.

Anomalous behaviour of chromium :

Chromium (₂₄Cr) has electronic configuration,

₂₄Cr (Expected) : 1s², 2s², 2p⁶, 3s², 3p⁶, 3d⁴, 4s²

       (Observed) : 1s², 2s², 2p⁶, 3s², 3p⁶, 3s², 4s¹

Explanation :

• The energy difference between 3d- and 4s-orbitals is very low.
• d-orbitals being degenerate, they acquire more stability when they are half-filled (3d⁵)
• Therefore, there arises a transfer of one electron from 4s-orbital to 3d-orbital in Cr giving more stable half-filled orbital. Hence, the configuration of Cr is [Ar] 3d⁵ 4s¹ and not [Ar] 3d⁴ 4s².
• This shows anomalous behaviour of chromium.

(a) n = 2, l = 1 the orbital is 2p

(b) n = 4, l = 2 the orbital is 4d

(c) n = 3, l = 2, the orbital is 3d

₂₆Fe  [Ar] 3d⁶ 4s²

Fe²⁺  [Ar] 3d⁶

Fe³⁺  [Ar] 3d⁵

(a) ₃Li  [He] 2s¹

(b) ₆C  [He] 2s² 2p²

(c) ₈O  [He] 2s² 2p⁴

(d) ₁₄Si  [Ne] 3s² 3p²

(8) ₁₇Cl  [Ne] 3s² 3p⁵

(f) ₂₀Ca  [Ar] 4s²

Azimuthal quantum number (l) : This represents the subsidiary quantum number or the subshell of the orbit to which the electron belongs. It is denoted by l. It is also called as secondary, subsidiary, orbital or angular momentum quantum number. It defines the shape of the orbital and the angular momentum of the electron. The value of l depends on principal quantum number n. It has positive values between 0 to (n — 1) :

This explains the significance of azimuthal quantum number

For n = 3, l = 0, 1, 2.

For l = 0, m_l = 0

For l = 1, m_l = −1, 0, +1

For l = 2, m_l = −2, −1, 0, +1

By Hund's rule,

 1s² 2s² 2p_x² 2p_y¹

The electronic configuration,

1s² 2s² 2p_x² 2p_y² 2p_z⁰  violates Hund's rule

Principal quantum number (n) : This describes the orbit or shell of an atom to which the electron belongs. It is represented by ‘n’ which has integral values. The energy of an electron depends on the value of n.

‘M’ shell has,

n = 3

l = 0, 1, 2

m_l : When l = 0, m_l = 0, m_s = \(±\frac{1}{2}\)

m_l : When l = 1, m_l = −1, 0, +1 m_s = \(±\frac{1}{2}\),\(±\frac{1}{2}\),\(±\frac{1}{2}\)

m_l : When l = 2, m_l = −2, −1, 0, +1, +2 m_s = \(±\frac{1}{2}\),\(±\frac{1}{2}\),\(±\frac{1}{2}\),\(±\frac{1}{2}\),\(±\frac{1}{2}\)

(a) ₁₄Si  [Ne] 3s² 3p_x¹; 3p_y¹;

Number of unpaired electrons = 2

(b) ₂₄Cr [Ar] 3d⁵ 4s¹

Number of unpaired electrons = 6

(a) Since atom has 29 electrons, it has 29 protons. The atomic number of the element is 29. It is copper.

(b) ∴ Electronic configuration : ₂₉Cu [Ar] 3d¹⁰ 4s¹.