Atoms Class 12 Notes | CBSE Physics Revision

Key Definitions

Atomic Number (Z)

The number of protons in the nucleus of an atom. It defines the element.

Mass Number (A)

The total number of protons and neutrons (nucleons) in the nucleus of an atom.

Isotopes

Atoms of the same element (same Z) but with different numbers of neutrons (different A).

Isobars

Atoms of different elements (different Z) but with the same mass number (same A).

Alpha Particle (α)

The nucleus of a Helium atom (₂He⁴), consisting of two protons and two neutrons, carrying a +2e charge.

Impact Parameter (b)

The perpendicular distance of the initial velocity vector of the alpha particle from the center of the nucleus in Rutherford's scattering experiment.

Excitation Energy

The energy required to move an electron from its ground state to a higher energy level (excited state).

Ionization Energy

The minimum energy required to remove an electron completely from an atom in its ground state, making it an ion.

Evolution of Atomic Models

Understanding the atom began with early conceptual models. Thomson's Plum Pudding Model (1898) proposed that an atom is a sphere of uniformly distributed positive charge, with electrons (negative charges) embedded within it, like plums in a pudding. This model successfully explained the overall neutrality of atoms but failed to explain more complex phenomena like the scattering of alpha particles.

The groundbreaking Rutherford's Nuclear Model (1911), based on the alpha-particle scattering experiment, revolutionized our understanding. Observations from scattering alpha particles off a thin gold foil led to several key conclusions:

• Most alpha particles passed undeflected, indicating that most of the atom is empty space.
• A few alpha particles were deflected at large angles, and a very small fraction even bounced back, suggesting a tiny, dense, positively charged core at the center, called the nucleus.
• The size of the nucleus is extremely small compared to the size of the atom (about 10⁻¹⁵ m vs 10⁻¹⁰ m).

Limitations of Rutherford's Model:

1. Atomic Stability: According to classical electromagnetic theory, an electron orbiting the nucleus should continuously radiate energy and spiral into the nucleus, making the atom unstable. However, atoms are stable.
2. Line Spectra: It could not explain the characteristic line spectra emitted by atoms; classical theory predicted a continuous spectrum.

Bohr's Model of the Hydrogen Atom

Hydrogen Spectral Series

Worked Example

• {"title":"Calculate the radius of the first Bohr orbit for the hydrogen atom.","bodyMarkdown":"Given: For hydrogen, Z=1. We need to find the radius for the first orbit, so n=1.\nFormula: r_n = 0.529 × 10⁻¹⁰ (n²/Z) m\nSolution:\nr₁ = 0.529 × 10⁻¹⁰ (1²/1) m\nr₁ = 0.529 × 10⁻¹⁰ m or 0.529 Å\nAnswer: The radius of the first Bohr orbit for hydrogen is approximately 0.529 Å."}

Key Points to Remember

• Rutherford's experiment proved the existence of a small, dense, positively charged nucleus.
• Bohr's model successfully explained the stability of atoms and the line spectra of hydrogen-like atoms.
• Angular momentum is quantized: L = n(h/2π).
• Energy levels are quantized and negative: E_n = -13.6 (Z²/n²) eV. Negative energy implies a bound state.
• Excitation energy is E_final - E_initial; ionization energy is 0 - E_ground_state = |E_ground_state|.
• The Rydberg formula 1/λ = RZ² (1/n_f² - 1/n_i²) is crucial for calculating spectral line wavelengths.
• Lyman series transitions end at n=1 (UV), Balmer at n=2 (Visible), and Paschen, Brackett, Pfund series end at n=3, 4, 5 respectively (IR).
• Bohr's model fails for multi-electron atoms and cannot explain the fine structure of spectral lines or Zeeman effect.

Section 7

When solving problems involving Bohr's model, pay close attention to units (eV, Joules, Angstroms, meters) and ensure consistent conversion. Remember that energy values are negative for bound electrons. Be prepared to derive expressions for radius, velocity, and energy, as these are common board exam questions. Also, practice problems involving transitions between energy levels to calculate emitted/absorbed photon energy and wavelength.

Practice Questions with Solutions

• Q: What were the two main limitations of Rutherford's atomic model? A: It could not explain the stability of atoms and it failed to account for the discrete line spectra observed from atoms.
• Q: State Bohr's postulate for the quantization of angular momentum. A: An electron can revolve only in those orbits where its angular momentum is an integral multiple of h/2π, i.e., mvr = n(h/2π).
• Q: Which spectral series of the hydrogen atom lies in the visible region? A: The Balmer series, which involves electron transitions ending at the n=2 energy level, lies in the visible region of the electromagnetic spectrum.
• Q: What is the physical significance of the negative sign in the expression for the electron's energy in Bohr's model? A: The negative sign indicates that the electron is bound to the nucleus, meaning energy must be supplied to remove it from the atom (to make it free).

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