Structure of Atom (Class 11)

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### Introduction to Atoms - **Atom:** The smallest unit of matter that retains an element's chemical identity. - **Early Theories:** - **Dalton's Atomic Theory (1808):** - Matter consists of indivisible atoms. - Atoms of same element are identical in mass & properties. - Atoms of different elements differ. - Atoms combine in simple whole-number ratios. - Atoms are neither created nor destroyed. - **Limitations:** Failed to explain subatomic particles, isotopes, and electrical nature of matter. ### Discovery of Subatomic Particles - **Electrons (e⁻):** - **Discovery:** J.J. Thomson (1897) using Cathode Ray Tube (CRT) experiment. - **Properties:** Negatively charged, mass $9.109 \times 10^{-31}$ kg, charge $-1.602 \times 10^{-19}$ C. - **Charge-to-mass ratio (e/m):** $1.7588 \times 10^{11}$ C/kg. - **Protons (p⁺):** - **Discovery:** E. Goldstein (1886) using modified CRT (anode rays/canal rays). Later characterized by Rutherford. - **Properties:** Positively charged, mass $1.672 \times 10^{-27}$ kg (approx. 1836 times electron mass), charge $+1.602 \times 10^{-19}$ C. - **Neutrons (n⁰):** - **Discovery:** James Chadwick (1932) by bombarding beryllium with alpha particles. - **Properties:** No charge (neutral), mass $1.674 \times 10^{-27}$ kg (slightly more than proton). | Particle | Symbol | Relative Charge | Absolute Charge (C) | Relative Mass (amu) | Absolute Mass (kg) | |----------|--------|-----------------|---------------------|---------------------|--------------------| | Electron | e⁻ | -1 | $-1.602 \times 10^{-19}$ | 0.000548 | $9.109 \times 10^{-31}$ | | Proton | p⁺ | +1 | $+1.602 \times 10^{-19}$ | 1.00727 | $1.672 \times 10^{-27}$ | | Neutron | n⁰ | 0 | 0 | 1.00867 | $1.674 \times 10^{-27}$ | ### Atomic Models #### 1. Thomson's Plum Pudding Model (1904) - **Concept:** Atom is a sphere of uniform positive charge with electrons embedded in it, like plums in a pudding. - **Limitations:** Failed to explain Rutherford's $\alpha$-scattering experiment. #### 2. Rutherford's Nuclear Model (1911) - **Experiment:** $\alpha$-scattering experiment (gold foil experiment). - Alpha particles (He²⁺) were bombarded on a thin gold foil. - **Observations:** - Most $\alpha$-particles passed undeflected. - A few were deflected at small angles. - Very few (1 in 20,000) bounced back (deflected at 180°). - **Conclusions:** - Most of the atom is empty space. - A small, dense, positively charged nucleus exists at the center. - Electrons revolve around the nucleus in circular paths. - **Postulates:** - Atom has a tiny, dense, positively charged nucleus. - Electrons revolve around the nucleus in orbits. - Electrostatic forces of attraction balance centrifugal force. - **Limitations:** - **Stability of atom:** According to Maxwell's electromagnetic theory, accelerating electrons should continuously emit radiation and spiral into the nucleus, making atoms unstable. - **Line spectrum:** Could not explain the discrete line spectra of elements. #### 3. Bohr's Model of Hydrogen Atom (1913) - **Postulates:** 1. Electrons revolve around the nucleus in specific, stable orbits (stationary states) without radiating energy. 2. Each orbit has a fixed energy, hence called energy levels or shells (K, L, M, N...). 3. Electrons can only exist in orbits where their angular momentum is an integral multiple of $h/2\pi$ (quantization of angular momentum): $m_e v r = n \frac{h}{2\pi}$, where $n = 1, 2, 3...$ (principal quantum number). 4. Energy is absorbed when an electron jumps from a lower to a higher orbit, and emitted when it drops from a higher to a lower orbit. The energy difference is given by $\Delta E = E_{final} - E_{initial} = h\nu$. - **Energy of an electron in nᵗʰ orbit:** $E_n = -R_H \left(\frac{1}{n^2}\right)$, where $R_H = 2.18 \times 10^{-18}$ J (Rydberg constant). For hydrogen-like species (e.g., He⁺, Li²⁺), $E_n = -R_H \left(\frac{Z^2}{n^2}\right)$. - **Radius of nᵗʰ orbit:** $r_n = 0.529 \times n^2/Z$ Å. - **Velocity of electron in nᵗʰ orbit:** $v_n = 2.18 \times 10^6 \times Z/n$ m/s. - **Limitations:** - Applicable only to single-electron species (e.g., H, He⁺, Li²⁺). - Failed to explain the fine structure of spectral lines (splitting of lines in magnetic field - Zeeman effect, and electric field - Stark effect). - Could not explain the ability of atoms to form molecules. ### Atomic Number & Mass Number - **Atomic Number (Z):** - Number of protons in the nucleus. - Defines the element. - For a neutral atom, Z = number of electrons. - **Mass Number (A):** - Total number of protons and neutrons in the nucleus. - $A = Z + N$ (where N is number of neutrons). - **Nuclide:** A specific type of atom characterized by its atomic number (Z) and mass number (A). Represented as $_Z^A X$. #### Isotopes, Isobars, Isotones, Isodiaphers - **Isotopes:** Atoms of the same element with the same atomic number (Z) but different mass numbers (A) due to different number of neutrons. - Example: $_1^1 H$ (Protium), $_1^2 H$ (Deuterium), $_1^3 H$ (Tritium) - **Isobars:** Atoms of different elements with the same mass number (A) but different atomic numbers (Z). - Example: $_{18}^{40} Ar$, $_{19}^{40} K$, $_{20}^{40} Ca$ - **Isotones:** Atoms of different elements with different atomic numbers (Z) and mass numbers (A) but the same number of neutrons (N). - Example: $_{14}^{30} Si$, $_{15}^{31} P$, $_{16}^{32} S$ (all have 16 neutrons) - **Isodiaphers:** Atoms of different elements with different atomic numbers and mass numbers but the same isotopic number (N-Z). - Example: $_{92}^{238} U$ (N-Z = 54), $_{90}^{234} Th$ (N-Z = 54) ### Electromagnetic Radiation (EMR) - **Wave Nature of Light:** - EMR propagates as waves, consisting of oscillating electric and magnetic fields perpendicular to each other and to the direction of propagation. - Travels at the speed of light, $c = 3 \times 10^8$ m/s in vacuum. - **Wavelength ($\lambda$):** Distance between two consecutive crests or troughs. Unit: m, nm, Å. - **Frequency ($\nu$):** Number of waves passing a point per second. Unit: Hz or s⁻¹. - **Wave number ($\bar{\nu}$):** Number of wavelengths per unit length. $\bar{\nu} = 1/\lambda$. Unit: m⁻¹, cm⁻¹. - **Relationship:** $c = \lambda\nu$. - **Electromagnetic Spectrum:** Arrangement of various types of EMR in order of increasing wavelength or decreasing frequency (e.g., Gamma rays ### Quantum Mechanical Model of Atom - **Concept:** Describes the behavior of electrons in atoms based on wave mechanics. - **Schrödinger Wave Equation:** - $H\psi = E\psi$, where $H$ is the Hamiltonian operator, $\psi$ is the wave function, and $E$ is the total energy. - **Wave function ($\psi$):** A mathematical function that describes the probability of finding an electron in a certain region of space. It has no physical significance by itself. - **Probability density ($\psi^2$):** Represents the probability of finding an electron at a particular point in space. - **Atomic Orbitals:** Three-dimensional regions around the nucleus where the probability of finding an electron is maximum. - **Difference from Bohr's orbits:** Orbits are fixed circular paths; orbitals are probability distributions. #### Quantum Numbers - Describe the state of an electron in an atom. Each electron in an atom has a unique set of four quantum numbers. 1. **Principal Quantum Number (n):** - **Value:** Positive integers (1, 2, 3, ...). - **Significance:** Determines the main energy level (shell) and the average distance of the electron from the nucleus. - Higher 'n' means higher energy and larger orbital size. - Max electrons in a shell = $2n^2$. 2. **Azimuthal (Angular Momentum) Quantum Number (l):** - **Value:** Integers from 0 to $(n-1)$ for a given 'n'. - **Significance:** Determines the shape of the orbital (subshell) and the angular momentum of the electron. - **l = 0:** s subshell (spherical shape) - **l = 1:** p subshell (dumbbell shape) - **l = 2:** d subshell (cloverleaf/double dumbbell shape) - **l = 3:** f subshell (complex shape) - Number of subshells in a shell = n. 3. **Magnetic Quantum Number ($m_l$):** - **Value:** Integers from $-l$ through 0 to $+l$. - **Significance:** Determines the orientation of the orbital in space. - For a given 'l', there are $(2l + 1)$ possible values of $m_l$, corresponding to $(2l + 1)$ orbitals in a subshell. - Example: - If l=0 (s subshell), $m_l=0$ (1 orbital) - If l=1 (p subshell), $m_l=-1, 0, +1$ (3 orbitals) - If l=2 (d subshell), $m_l=-2, -1, 0, +1, +2$ (5 orbitals) 4. **Spin Quantum Number ($m_s$):** - **Value:** $+1/2$ or $-1/2$. - **Significance:** Describes the intrinsic angular momentum (spin) of the electron, which creates a magnetic field. - Represented by $\uparrow$ (spin up) or $\downarrow$ (spin down). #### Shapes of Atomic Orbitals - **s-orbitals:** Spherically symmetrical. The probability of finding the electron is equal in all directions at a given distance from the nucleus. - 1s, 2s, 3s... are all spherical but 2s is larger than 1s, 3s is larger than 2s. - **p-orbitals:** Dumbbell-shaped. Each subshell has three p-orbitals ($p_x, p_y, p_z$) oriented along the x, y, and z axes. They are degenerate (have the same energy) in the absence of an external magnetic field. - **d-orbitals:** Five d-orbitals in a d subshell. Four of them ($d_{xy}, d_{yz}, d_{xz}, d_{x^2-y^2}$) have cloverleaf shapes, while the fifth ($d_{z^2}$) has a dumbbell shape with a donut around the middle. #### Pauli's Exclusion Principle - **Statement:** No two electrons in an atom can have the same set of all four quantum numbers. - **Implication:** An atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins. #### Aufbau Principle - **Statement:** In the ground state of an atom, electrons fill atomic orbitals in order of increasing energy. - **Order of filling:** 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p... - **(n+l) rule:** Orbitals with lower (n+l) value are filled first. If (n+l) values are same, the orbital with lower 'n' value is filled first. - Example: For 3d, n=3, l=2, so n+l=5. For 4s, n=4, l=0, so n+l=4. Thus, 4s is filled before 3d. #### Hund's Rule of Maximum Multiplicity - **Statement:** Pairing of electrons in degenerate orbitals (orbitals of the same energy, e.g., $p_x, p_y, p_z$) does not occur until each orbital in that subshell is singly occupied with parallel spins. - **Implication:** Electrons prefer to remain unpaired as much as possible to minimize electron-electron repulsion and achieve greater stability. - Example: For Nitrogen (7 electrons): 1s² 2s² 2p³ (each 2p orbital gets one electron with parallel spin before any pairing occurs). #### Electronic Configuration - The distribution of electrons into orbitals of an atom. - **Example:** - H (Z=1): $1s^1$ - He (Z=2): $1s^2$ - C (Z=6): $1s^2 2s^2 2p^2$ - O (Z=8): $1s^2 2s^2 2p^4$ - Na (Z=11): $1s^2 2s^2 2p^6 3s^1$ or [Ne]$3s^1$ (using noble gas core) #### Stability of Half-filled and Fully-filled Orbitals - Orbitals that are completely half-filled (e.g., $p^3, d^5, f^7$) or fully-filled (e.g., $p^6, d^{10}, f^{14}$) exhibit extra stability. - **Reasons:** 1. **Symmetry:** Symmetrical distribution of electrons leads to greater stability. 2. **Exchange Energy:** Electrons with parallel spins in degenerate orbitals can exchange their positions. The greater the number of possible exchanges, the greater the exchange energy, and thus greater the stability. - **Exceptions to Aufbau Principle:** - **Chromium (Cr, Z=24):** Expected $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^4$. Actual is $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^5$ (half-filled d-orbital gives extra stability). - **Copper (Cu, Z=29):** Expected $1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^9$. Actual is $1s^2 2s^2 2p^6 3s^2 3p^6 4s^1 3d^{10}$ (fully-filled d-orbital gives extra stability).