Frequently Asked Questions
Rutherford’s gold foil experiment showed that a small fraction of a-particles were deflected at very large angles (even rebounding), indicating that positive charge and most of the mass are concentrated in a tiny nucleus, contradicting Thomson’s uniform charge distribution model.
Bohr’s model assumes a single electron moving under Coulombic attraction. Helium has two electrons, and electron–electron repulsion is not considered in Bohr’s theory, making it valid only for hydrogen-like (one-electron) species.
The principal quantum number \( n \) determines the size and energy of an orbital. Larger \( n \) values correspond to orbitals farther from the nucleus and higher energy levels.
As \( n \to \infty \), the energy difference between successive levels decreases according to \( E_n = -\frac{13.6}{n^2} \, \text{eV} \). Therefore, spectral lines become closer and converge at the series limit.
In neutral atoms, 4s fills first due to lower \( n + l \) value. After ionization, 3d orbitals experience greater effective nuclear charge and become lower in energy, so electrons are removed from 4s first.
The Rydberg constant depends on reduced mass \( \mu = \frac{m_e M}{m_e + M} \). For heavier nuclei, slight changes in \( \mu \) cause small shifts in spectral lines.
s-orbitals have non-zero electron density at the nucleus (\( \psi^2 \neq 0 \) at \( r=0 \)), allowing greater penetration and stronger nuclear attraction compared to p-orbitals.
Degenerate orbitals are orbitals having equal energy. In hydrogen, all orbitals with the same \( n \) are degenerate, but in multi-electron atoms, energies depend on both \( n \) and \( l \).
Quantum mechanics gives angular momentum magnitude as \( L = \sqrt{l(l+1)}\hbar \), where \( l = 0,1,2,\dots,(n-1) \). Boundary conditions on wave functions lead to discrete allowed values.
According to \( \Delta x \, \Delta p \ge \frac{\hbar}{2} \), for very small mass (like electrons), uncertainties in position and momentum are significant, whereas for macroscopic objects they are negligible.
Moseley showed that X-ray frequency follows \( \nu = a(Z - b)^2 \), proving that atomic number \( Z \) (nuclear charge), not atomic mass, determines elemental identity.
Electron spin explains fine spectral splitting and supports Pauli’s exclusion principle, which states that no two electrons can have the same set of four quantum numbers.
Both involve transitions between the same quantized energy levels. Absorption excites electrons upward, while emission occurs when electrons return to lower levels.
Isotones have equal neutron number but different atomic numbers. Chemical properties depend on electronic configuration, which changes with atomic number.
Increased inner-shell electrons shield valence electrons from nuclear attraction, reducing effective nuclear charge and lowering ionization enthalpy.