Alpha particles are directed at a thin gold foil in a vacuum. A surrounding fluorescent screen detects the alpha particles after they pass near or through the foil.

The visible spectrum from a hot, low-pressure gas contains bright lines at particular wavelengths on a dark background.

A sample in a flame produces emission lines at $486\ \text{nm}$, $589\ \text{nm}$ and $656\ \text{nm}$. Laboratory reference lines include hydrogen at $486\ \text{nm}$ and $656\ \text{nm}$, sodium at $589\ \text{nm}$, and calcium at $422\ \text{nm}$ and $616\ \text{nm}$.

White light passes through a cool, low-pressure gas and then into a spectrometer. Dark lines are observed in the otherwise continuous spectrum.

Rutherford scattering predictions agree with observations for alpha particles of relatively low kinetic energy, but deviations are observed when the incident alpha-particle energy is increased sufficiently.

For hydrogen, the Bohr energy levels are given by $E_n=-13.6/n^2\ \text{eV}$.

Alpha particles were directed at a very thin gold foil. A detector counted scintillations at different angles from the original alpha-particle direction.

A mass spectrometer separates neutral atoms of a sample into three isotope peaks. The chemical symbol $X$ is supplied for the element.

A narrow beam containing photons of several frequencies passes through a cool low-pressure gas. The spectrum is recorded in the original beam direction and also at $90^\circ$ to the beam.

An atom has allowed energy levels at $-5.20\ \text{eV}$, $-3.10\ \text{eV}$ and $-1.60\ \text{eV}$. A beam of monochromatic photons of wavelength $590\ \text{nm}$ is incident on atoms initially in the lowest of these levels. Use $hc=1.24\times10^{-6}\ \text{eV m}$.

A nucleus has nucleon number $A=64$. Assume that the nuclear radius is given by $R=R_0A^{1/3}$, where $R_0=1.20\times10^{-15}\ \text{m}$. The unified atomic mass unit is $u=1.66\times10^{-27}\ \text{kg}$.

In the Bohr model of hydrogen, the energy of level $n$ is $E_n=-13.6/n^2\ \text{eV}$. An excited hydrogen atom makes a transition from $n=4$ to $n=2$. Use $hc=1.24\times10^{-6}\ \text{eV m}$.

In the de Broglie interpretation of the Bohr model, an allowed electron orbit forms a standing wave around the circumference of the orbit. For one allowed orbit in hydrogen, $n=3$ and $r=4.76\times10^{-10}\ \text{m}$. Use $m_e=9.11\times10^{-31}\ \text{kg}$ and $h=6.63\times10^{-34}\ \text{J s}$.

The spectra of a hot low-pressure gas and of a continuous source viewed through a cooler sample of the same gas are shown.

An atom has the allowed energy levels shown. A transition labelled T occurs from level $E_3$ to level $E_1$. Use $hc=1.24\times10^{-6}\ \text{eV m}$.

The absorption spectrum of light from a star is compared with laboratory emission spectra for three elements.

An alpha particle of kinetic energy $5.00\ \text{MeV}$ approaches a stationary gold nucleus head-on. The proton number of gold is $79$. Use $k=8.99\times10^9\ \text{N m}^2\text{C}^{-2}$, $e=1.60\times10^{-19}\ \text{C}$ and $1\ \text{MeV}=1.60\times10^{-13}\ \text{J}$.

Measurements of nuclear radius $R$ for several nuclei are plotted against $A^{1/3}$, where $A$ is the nucleon number. Assume the nuclei are spherical and use $u=1.66\times10^{-27}\ \text{kg}$.

Alpha particles are scattered by a gold foil. The graph compares the Rutherford prediction with the measured fraction of alpha particles scattered through angles greater than $90^\circ$ as the alpha-particle kinetic energy is increased. For gold, $Z=79$.

An alpha particle approaches a copper nucleus head-on. In the model, the copper nucleus does not recoil and the interaction is only electric repulsion. For copper, $Z=29$.

The diagram shows some energy levels of hydrogen in the Bohr model. Use $E_n=-13.6/n^2\ \text{eV}$ and $hc=1.24\times10^{-6}\ \text{eV m}$.

A narrow beam of alpha particles is directed at a very thin gold foil in an evacuated chamber. A movable fluorescent screen detects the alpha particles after they interact with the foil.

Two neutral atoms are represented by the nuclear notation ${}^{63}_{29}X$ and ${}^{65}_{29}X$. The chemical symbol $X$ is not required.

Several models have been used to describe atoms. A simple hard-sphere model can be useful in kinetic theory, the Thomson model included electrons embedded in positive charge, and the Rutherford model introduced a small central nucleus.

In the Bohr model, an allowed electron orbit may be represented by a standing de Broglie wave around a circular path. For the orbit shown, $n=3$ and $r=4.76\times10^{-10}\ \text{m}$. Use $h=6.63\times10^{-34}\ \text{J s}$ and $m_e=9.11\times10^{-31}\ \text{kg}$.

High-resolution spectra are compared with predictions from the Bohr model.

A low-pressure gas is placed in a discharge tube. The light from the tube is viewed through a spectrometer. Several bright lines are observed against a dark background.

The absorption spectrum of light from a star is compared with laboratory spectra of three elements. Several dark lines in the star spectrum coincide with lines in the laboratory spectra.

An atom has three allowed energy levels: ground state $E_1=0$, first excited state $E_2=2.10\ \text{eV}$ and second excited state $E_3=4.00\ \text{eV}$. The zero of energy is chosen at the ground state for this question.

For a ${}^{208}_{82}\text{Pb}$ nucleus, the radius $R$ is modelled by $R=R_0A^{1/3}$, where $R_0=1.20\times 10^{-15}\ \text{m}$. The mass of one nucleon may be taken as $1.66\times 10^{-27}\ \text{kg}$.

An alpha particle with kinetic energy $5.0\ \text{MeV}$ is directed head-on towards a stationary gold nucleus with proton number $Z=79$. Assume that only electric repulsion acts and that the gold nucleus does not recoil.

In the Bohr model for hydrogen the energy of level $n$ is $E_n=-13.6/n^2\ \text{eV}$.

Alpha particles of increasing kinetic energy are scattered by a thin metal foil. At low energies the angular distribution agrees with Rutherford scattering, but above a certain energy the measured distribution begins to differ from the Rutherford prediction.

Bohr proposed that the angular momentum of the electron in a hydrogen atom is quantized according to $mvr=nh/(2\pi)$. A de Broglie interpretation treats the electron as a wave around a circular orbit.

A simplified hydrogen atom is initially in the $n=4$ state. In the Bohr model for hydrogen, $E_n=-13.6/n^2\ \text{eV}$ and the zero of energy corresponds to ionization.