Atoms

The One Thing

Rutherford established that an atom is mostly empty space with nearly all its mass and positive charge concentrated in a tiny nucleus. Bohr explained atomic stability and hydrogen’s discrete line spectrum by proposing quantised electron orbits, with radiation emitted or absorbed only when electrons transition between allowed energy levels.

Reactions, Processes and Experiments

Key Terms

• Rutherford atomic model: An atomic model in which nearly all positive charge and mass are concentrated in a small central nucleus, with electrons revolving around it.
• Alpha-particle scattering experiment: An experiment in which alpha particles were directed at a thin gold foil; most passed straight through, some were deflected, and a very small number bounced back.
• Nucleus: The tiny, positively charged central region of an atom containing almost all its mass.
• Nuclear size: The nuclear radius is of the order of $10^{-15}\mathrm{m}$, while the atomic radius is of the order of $10^{-10}\mathrm{m}$.
• Limitations of Rutherford model: According to classical electromagnetic theory, a revolving electron should continuously radiate energy, lose speed, and spiral into the nucleus; the model also could not explain line spectra.
• Bohr model: A model in which electrons move only in certain permitted circular orbits called stationary orbits, without continuously radiating energy.
• Stationary orbit: An allowed orbit in which an electron has a definite energy and does not radiate energy.
• Quantisation of angular momentum: The electron’s angular momentum can have only the values $mvr=nh/(2\pi )=n\hslash$, where $n=1,2,3,...$.
• Principal quantum number: The positive integer $n$ that identifies an allowed energy level or shell; $n=1,2,3,...$.
• Bohr radius: The radius of the first permitted orbit of hydrogen, $a_0=0.529\text{A˚}=5.29\times 10^{-11}\mathrm{m}$.
• Energy of hydrogen atom: For the $n$th orbit, $E_n=-13.6/n^2\mathrm{eV}=-2.18\times 10^{-18}/n^2\mathrm{J}$. The negative sign indicates a bound electron.
• Ground state: The lowest-energy state of an atom, corresponding to $n=1$ for hydrogen.
• Excited state: Any state with energy higher than the ground state, corresponding to $n>1$.
• Ionisation energy: The minimum energy required to remove an electron completely from an atom in its ground state; for hydrogen it is $13.6\mathrm{eV}$.
• Excitation energy: The energy needed to raise an electron from one allowed energy level to a higher level.
• Photon emission: When an electron moves from a higher energy level to a lower level, it emits a photon whose energy is $h\nu =E_i-E_f$.
• Photon absorption: When an electron absorbs a photon of exactly the required energy, it moves from a lower energy level to a higher level.
• Hydrogen line spectrum: A set of discrete bright lines produced when excited hydrogen atoms emit radiation at specific wavelengths.
• Rydberg formula: For hydrogen spectral lines, $1/\lambda =R(1/n_f^2-1/n_i^2)$, where $n_i>n_f$ and $R\approx 1.097\times 10^7{\mathrm{m}}^{-1}$.
• Spectral series: A group of hydrogen spectral lines formed when electrons fall to the same final energy level.
• Lyman series: Transitions ending at $n=1$; these lines lie in the ultraviolet region.
• Balmer series: Transitions ending at $n=2$; several lines lie in the visible region.
• Paschen series: Transitions ending at $n=3$; these lines lie in the infrared region.
• Brackett series: Transitions ending at $n=4$; these lines lie in the infrared region.
• Pfund series: Transitions ending at $n=5$; these lines lie in the infrared region.
• Reduced mass correction: For greater accuracy, the electron mass in hydrogen formulas is replaced by the reduced mass of the electron-proton system.
• de Broglie explanation of Bohr orbit: An allowed orbit contains a whole number of electron wavelengths, so $2\pi r=n\lambda$, which leads to quantised angular momentum.

Easily Confused

• Rutherford model and Bohr model: Rutherford proposed a nuclear atom but could not explain atomic stability or line spectra; Bohr introduced stationary orbits and quantised energy levels.
• Ground state and excited state: The ground state has $n=1$ and the lowest energy; an excited state has $n>1$ and higher energy.
• Ionisation energy and excitation energy: Ionisation energy removes an electron completely from the atom; excitation energy raises it to a higher allowed level.
• Photon emission and photon absorption: Emission occurs when an electron moves from a higher to a lower level; absorption occurs when it moves from a lower to a higher level.
• Shortest and longest wavelength in a spectral series: The series limit gives the shortest wavelength, whereas the smallest transition energy into the final level gives the longest wavelength.
• Lyman, Balmer and Paschen series: Lyman transitions end at $n=1$ and are ultraviolet; Balmer transitions end at $n=2$ and include visible lines; Paschen transitions end at $n=3$ and are infrared.
• Bohr radius and nuclear radius: The Bohr radius is $5.29\times 10^{-11}\mathrm{m}$, whereas the nuclear radius is of the order of $10^{-15}\mathrm{m}$.
• Rutherford’s classical prediction and Bohr’s postulate: Classical theory predicts that a revolving electron radiates continuously and spirals into the nucleus; Bohr’s model states that stationary orbits do not radiate.

What Gets Asked

• Explain Rutherford’s gold-foil experiment and its conclusions. Marks depend on identifying alpha particles, the thin gold foil, the fact that most passed undeflected, and the small number of large-angle deflections or rebounds.
• State the limitations of Rutherford’s model. The required points are the predicted continuous radiation and collapse of the revolving electron, together with the model’s inability to explain line spectra.
• Use Bohr’s quantisation condition and hydrogen-orbit equations. Questions may require $mvr=nh/(2\pi )=n\hslash$, $r_n=a_0{n}^2$, $r_n=a_0{n}^2/Z$, or $v_n=2.18\times 10^6/n{\mathrm{ms}}^{-1}$; omitting the role of $n$ or $Z$ loses accuracy.
• Calculate energy changes and identify emission or absorption. For emission, the electron moves from $n_i$ to $n_f$ with $n_i>n_f$, and $\Delta E=E_i-E_f=h\nu$; absorption requires the reverse direction and an exact photon energy.
• Apply the Rydberg formula to hydrogen spectral lines. The final level $n_f$ identifies the spectral series, and the formula requires $n_i>n_f$: $1/\lambda =R(1/n_f^2-1/n_i^2)$.
• Identify spectral-series limits and characteristic lines. The Balmer series ends at $n=2$, and the H-alpha line is the transition $n=3$ to $n=2$, with wavelength approximately $656.3\mathrm{nm}$; confusing the final level with the initial level costs marks.