CBSE Class 12 Physics Notes Chapter 12 Atoms

Atoms are the basic building blocks of matter. They are composed of subatomic particles, including protons, neutrons, and electrons. 

• Atoms consist of a nucleus at the center, made up of protons and neutrons, surrounded by orbiting electrons. 
• The nucleus carries a positive charge due to protons, while electrons carry a negative charge and orbit around the nucleus.
• Atoms are electrically neutral, meaning the number of protons in the nucleus equals the number of electrons orbiting around it. 
• The arrangement and movement of these subatomic particles determine the chemical properties of an element.

Structure of an atom given by different scientists are discussed below

• Thomson's Plum Pudding Model: Proposed by J.J. Thomson in 1898, the plum pudding model suggested that atoms have a positively charged mass with negatively charged electrons scattered within it.
  • It resembles "seeds in a watermelon." 
• Rutherford's Nuclear Model: Ernst Rutherford's 1906 experiment, later conducted by Geiger and Marsden, led to the formulation of the nuclear model of the atom. 
  • In this model, the positive charge and most of the mass are concentrated in a small nucleus, with electrons orbiting around it, akin to planets around the sun.
• Despite its advancement, Rutherford's model failed to explain why atoms emit light of only discrete wavelengths, particularly seen in hydrogen. 

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Class 12 Physics Chapter 12 Notes – Atoms

Alpha-Particle Scattering And Rutherford’s Nuclear Model Of Atom

• Conducted in 1911, Geiger and Marsden's experiment involved bombarding a thin gold foil with alpha particles emitted from a radioactive source.
• Observations revealed that most alpha particles passed through the foil, while a small fraction underwent significant deflections.
• This indicated the presence of a dense, positively charged nucleus.
• Based on the experimental results, Rutherford proposed a nuclear model of the atom, where the majority of the atom's mass and positive charge are concentrated in a tiny nucleus, with electrons orbiting around it.
• Rutherford estimated the size of the nucleus to be about 10-15 to 10−14 meters, significantly smaller than the overall size of the atom.
• Despite the dense nucleus, atoms are mostly empty space, with electrons orbiting far away from the nucleus. 
• Most alpha particles pass through atoms unaffected due to this emptiness, while those interacting with the nucleus experience significant deflections.

Alpha-Particle Trajectory

• The trajectory of an alpha particle during scattering depends on its impact parameter.
• Impact parameter is the perpendicular distance between the initial velocity vector of the particle and the center of the nucleus.

Impact Parameter Formula

• Formula:

b = ze² cot(θ/2) / 4πϵ_oE

Where

• z is the atomic number
• e is the charge
• θ is the scattering angle
• E is the kinetic energy

• Different impact parameters result in various scattering outcomes, ranging from large deflections for particles close to the nucleus to minimal deflections for those with larger impact parameters.
• The small fraction of alpha particles that rebound back suggests that head-on collisions, where the impact parameter is minimal, are infrequent. 
• This indicates that the mass and positive charge of the atom are concentrated in a small volume, allowing for a determination of the nucleus's upper size limit through Rutherford scattering.

Electron Orbits

• Rutherford Model Description: The Rutherford nuclear model depicts the atom as a neutral sphere with a small, massive, positively charged nucleus at the center, surrounded by electrons orbiting in stable paths.
• Electrostatic Balance in Orbits: In a hydrogen atom, the electrostatic force of attraction between the electrons and the nucleus balances the centripetal force required to keep the electrons in their orbits.
• Energy Considerations: The total energy of the electron in a hydrogen atom is negative, indicating its bound state to the nucleus. If the total energy were positive, the electron would not maintain a closed orbit around the nucleus.

Atomic Spectra

• Excited atomic gases emit radiation with specific wavelengths, creating an emission line spectrum characterized by bright lines against a dark background.
• Each element has a unique emission line spectrum, serving as a distinctive "fingerprint" for gas identification.
• When white light passes through a gas, dark lines appear in the spectrum, corresponding to wavelengths absorbed by the gas, mirroring those found in its emission line spectrum. 
• This phenomenon is known as the absorption spectrum.

Bohr Model Of Hydrogen Atom

• The classical model proposed by Rutherford portrays the atom as a miniature solar system, but it faces critical issues due to classical electromagnetic theory.
• Niels Bohr introduced key modifications to Rutherford's model by incorporating quantum concepts. 
• He postulated three fundamental ideas to explain atomic structure and spectra.
• First Postulate: Electrons can revolve in stable orbits without emitting radiation, contrary to classical predictions.
• Second Postulate: Electrons orbit only in quantized orbits where angular momentum is an integral multiple of h/2π.
• Third Postulate: Electrons can transition between non-radiating orbits, emitting photons with energy equal to the energy difference of the initial and final states.

Bohr’s Theory of Hydrogen atom

• Radius of an orbit Formula:

r_n = n²r_o

Where

• r_n is the radius of n^th orbit
• n is the principal quantum number
• r_o is Bohr’s radius

• Speed of electron in an orbit Formula:

v_n = (2.18 x 10⁶) / n

Where v_n is the speed of the electron in n^th orbit

• Enery of an electron in an orbit Formula:

E_n = - (13.6 / n²) eV

Where E_n is the total energy of an electron in n^th orbit

Drawbacks of Bohr’s Atomic Model

• It is only valid for one electron atoms.
• Orbits were taken as circular but according to Sommerfield these are elliptical.
• Intensity of spectral lines could not be explained.
• Nucleus was taken as stationary but it also rotates on its own axis.
• It could explain the fine structure in spectrum line.
• It does explain the Zeeman effect and Strak effect.

Energy Levels

• The energy of a hydrogen atom in nth orbit is given by

E_n = -(13.6 / n²) eV

• In Bohr's model, energy decreases as the electron orbits closer to the nucleus, with the ground state possessing the lowest energy at n = 1 and progressively higher energy levels for larger n.
• The ionization energy of hydrogen, predicted by Bohr's model as 13.6 eV, is the energy required to free an electron from the ground state.
• When hydrogen atoms absorb energy, electrons transition to higher energy states (excited states). 
• As they return to lower energy states, photons are emitted. 
• The energy difference between states determines photon energy.

Line Spectra Of Hydrogen Atom

• Electrons in hydrogen atoms emit photons when transitioning from higher to lower energy states.
• This results in discrete frequencies known as emission lines.
• Absorption occurs when atoms absorb photons matching the energy needed for electron transitions.
• It produces dark absorption lines in a continuous spectrum.
• Bohr's model successfully explains the hydrogen atom spectrum, distinguishing between emission and absorption phenomena.

Rydberg Formula for Hydrogen Atom

• Formula:

1/λ = RZ² (1/n²_f - 1/n²_i)

Where

• λ is the wavelength of the emitted light
• R is Rydberg’s constant = 1.097 x 10⁷ m^-1
• Z is the atomic number
• n_i is the initial energy state
• n_f is the final energy state

Spectral Series of Hydrogen Atom

• Lyman Series: Spectral lines emitted when electrons travels from n_i = 2, 3, 4…. to n_f = 1.
• Balmer Series: Spectral lines emitted when electrons travels from n_i = 3, 4, 5…. to n_f = 2.
• Paschen Series: Spectral lines emitted when electrons travels from n_i = 4, 5, 6…. to n_f = 3.
• Brackett Series: Spectral lines emitted when electrons travels from n_i = 5, 6, 7…. to n_f = 4.
• Pfund Series: Spectral lines emitted when electrons travels from n_i = 6, 7, 8…. to n_f = 5.

De Broglie’s Explanation Of Bohr’s Second Postulate Of Quantisation

• De Broglie proposed that electrons in Bohr's model behave like particle waves, forming standing waves in circular orbits.
• Standing waves occur when the circumference of the electron's orbit equals an integer multiple of its de Broglie wavelength.
• De Broglie's hypothesis yields the quantum condition mvrn = nh/2π, explaining the quantization of angular momentum in electron orbits.

Important Terms Related to Atom

• Excitation: The process of absorption of energy by an electron.
• Excitation Energy: Amount of energy required by an electron to jump from ground energy state to higher energy state.
• Excitation Potential: Potential difference through which an electron must be accelerated to go from ground energy state to higher energy state.
• Ionization: The process of detaching an electron from an atom.
• Ionization Energy: The energy required to detach an electron from an atom.