Atoms and Atomic Models

Flashcards covering key definitions, principles, formulas, and spectral series from the lecture notes on atomic structure, including Dalton's model, Thomson's model, Rutherford's alpha-scattering experiment, and the Bohr atomic model.

Atom

The fundamental unit of matter.

Dalton's Atomic Theory

The atomic model proposing that all matter is made up of indivisible particles called atoms that cannot be subdivided.

Plum Pudding Model (Watermelon Model)

J.J. Thomson's atomic model in which negative charges (electrons) are embedded like seeds throughout a region of positive charge (pulp).

Zinc Sulphide ($\text{ZnS}$) Screen

A screen in Rutherford's $\alpha$-scattering experiment that produces scintillations when struck by scattered $\alpha$-particles, which are then observed through a microscope.

Number of Scattered $\alpha$-Particles ($N$)

The distribution of $\alpha$-particles scattered at an angle $\theta$, governed by the proportionality N \tag*{} \propto \frac{1}{\sin^4(\theta/2)}.

Atomic Nucleus (Rutherford Model)

A tightly concentrated central region containing the atom's positive charge and greater part of its mass, with a size of about $10^{-15}\,\text{m}$ to $10^{-14}\,\text{m}$, which is $10{,}000$ to $100{,}000$ times smaller than the atom ($10^{-10}\,\text{m}$).

Distance of Closest Approach ($r_0$)

The minimum distance from the nucleus to which an $\alpha$-particle can approach before its entire kinetic energy is converted into electrostatic potential energy, given by $r_0 = \frac{1}{4\pi\varepsilon_0}\frac{2Ze^2}{\frac{1}{2}mv^2} = \frac{Ze^2}{\pi\varepsilon_0 mv^2}$.

Impact Parameter ($b$)

The perpendicular distance of the initial velocity vector of an $\alpha$-particle from the centre of the target nucleus, given by $b = \frac{Ze^2\cot(\theta/2)}{4\pi\varepsilon_0\left(\frac{1}{2}mv^2\right)}$.

Total Energy of Orbiting Electron (Rutherford Model)

The sum of kinetic and potential energy for an electron revolving around a hydrogen nucleus ($Z = 1$), given by $T = -\frac{e^2}{8\pi\varepsilon_0 r}$, where the negative sign substantiates that the electron is bound to the nucleus.

Classical Electrodynamic Instability

A major drawback of Rutherford's model stating that an accelerated charged electron should continuously radiate energy, causing its orbit to spiral inward until it collapses into the nucleus.

Stationary Orbits

Discrete circular orbits proposed in Bohr's first postulate in which revolving electrons do not radiate energy.

Bohr's Quantisation Condition

Bohr's second postulate stating that the orbital angular momentum ($L$) of an electron in a stationary orbit is an integral multiple of $\frac{h}{2\pi}$, expressed as $L = mvr = \frac{nh}{2\pi}$.

Bohr's Frequency Condition

Bohr's third postulate stating that when an electron transitions between two stationary orbits, a photon is emitted with energy equal to the difference between the two states: $E_i - E_f = h\nu$.

Bohr Radius ($a_0$)

The radius of the innermost stationary orbit ($n = 1$) of the hydrogen atom ($Z = 1$), defined as $a_0 = \frac{h^2\varepsilon_0}{\pi m e^2} = 0.53\,\text{Å}$.

Electron Orbital Velocity ($v_n$)

The linear velocity of an electron in the $n^{\text{th}}$ Bohr orbit, expressed as $v_n = \frac{Ze^2}{2\varepsilon_0 nh} = \frac{c}{137}\frac{Z}{n}$.

Orbital Electric Current ($i_n$)

The equivalent current produced by the periodic motion of an electron in the $n^{\text{th}}$ Bohr orbit, calculated as $i_n = \frac{e}{T_n} = ef_n = 1.06\frac{Z^2}{n^3}\,\text{mA}$.

Total Energy in the $n^{\text{th}}$ Orbit ($E_n$)

The total energy of an electron in the $n^{\text{th}}$ Bohr orbit of a hydrogen atom, given by $E_n = -\frac{me^4}{8\varepsilon_0^2 n^2 h^2} = -\frac{13.6}{n^2}\,\text{eV}$.

Rydberg Constant ($R$)

The physical constant appearing in the spectral line wavenumber relation, defined as $R = \frac{me^4}{8\varepsilon_0^2 h^3 c} = 1.097 \times 10^7\,\text{m}^{-1}$.

Lyman Series

The spectral series of hydrogen corresponding to electron transitions to the ground state ($n_f = 1$) from higher levels ($n_i = 2, 3, 4, \dots$), falling in the ultraviolet (UV) region.

Balmer Series

The spectral series of hydrogen corresponding to electron transitions to the second level ($n_f = 2$) from higher levels ($n_i = 3, 4, 5, \dots$), falling in the visible region.

Paschen Series

The spectral series of hydrogen corresponding to electron transitions to the third level ($n_f = 3$) from higher levels ($n_i = 4, 5, 6, \dots$), falling in the near-infrared (near IR) region.

Brackett Series

The spectral series of hydrogen corresponding to electron transitions to the fourth level ($n_f = 4$) from higher levels ($n_i = 5, 6, 7, \dots$), falling in the mid-infrared (mid IR) region.

Pfund Series

The spectral series of hydrogen corresponding to electron transitions to the fifth level ($n_f = 5$) from higher levels ($n_i = 6, 7, 8, \dots$), falling in the far-infrared (far IR) region.

de Broglie's Explanation of Quantisation

The derivation of Bohr's angular momentum quantisation by treating the electron's orbit as a circular standing wave where the orbit circumference equals an integral number of de Broglie wavelengths ($2\pi r_n = n\lambda$).