E.1 Structure of the atom

A nucleus of iodine is represented by ¹²⁷₅₃I.

Which row gives the number of protons and the number of neutrons in this nucleus?

In a Geiger–Marsden–Rutherford experiment, alpha particles are directed at a thin gold foil. The diagrams show possible paths of one alpha particle that passes close to a single gold nucleus N.

Which diagram shows a possible path?

An electron in an atom falls from an energy level E₂ to a lower energy level E₁.

What is the wavelength of the photon emitted? (h is the Planck constant and c is the speed of light.)

The diagram shows the emission spectrum of a gas. All four bright lines are produced by transitions that end on the ground state.

White light passes through a cool sample of the same gas. Which spectrum shows the light that emerges?

A nucleus of nuclide X is represented by ^A_ZX. A nucleus of nuclide Y contains twice as many protons as the nucleus of X and the same number of neutrons.

What is the nucleon number of Y?

A neutral atom of the nuclide ^A_ZX gains two electrons and becomes a negative ion.

How many charged particles does the ion contain?

A nucleus of iron is represented by ⁵⁶₂₆Fe.

What is the best estimate of the mass of this nucleus? (1 u = 1.661 × 10⁻²⁷ kg)

In a Geiger–Marsden–Rutherford experiment, alpha particles are directed at a thin gold foil in a vacuum. A detector counts the number N of alpha particles scattered through an angle θ in equal time intervals, for θ from 10° to 170°.

Which graph shows how N varies with θ?

Which graph shows how the energy E of a photon varies with its wavelength λ?

A bicycle light contains a blue LED that emits photons of energy 2.6 eV and a red LED that emits photons of energy 1.9 eV. What is the ratio \(\frac{\text{wavelength of red light}}{\text{wavelength of blue light}}\)?

In a hydrogen discharge tube used for teaching, the applied voltage is adjusted so that electrons in the excited atoms reach the n = 3 level and no higher. All atoms then return to the ground state (n = 1). How many different wavelengths can be emitted?

A student looks at the light from a neon advertising sign through a diffraction grating. She sees a set of bright, sharp coloured lines separated by dark gaps. What does this observation provide direct evidence for?

Astronomers study light from a star that has passed through the atmosphere of an orbiting exoplanet. They compare the dark absorption lines of one element in the atmosphere with the bright emission lines of the same element measured in a laboratory. Any motion of the star and planet relative to Earth can be ignored. Which statement is correct?

Starlight in a nebula has excited some hydrogen atoms into the n = 2 level. The energy levels of hydrogen are −13.6 eV for n = 1 and −3.40 eV for n = 2. What is the minimum energy needed to ionize a hydrogen atom that is in the n = 2 level?

A shop sign uses a glass tube of low-pressure neon gas through which a current passes. What is the appearance of the spectrum of the light from the tube, and why?

Strontium salts give fireworks a deep red colour. What determines the wavelength of the red light emitted by the strontium atoms?

In the Geiger–Marsden experiment, a beam of alpha particles was directed at a thin gold foil. The great majority of the alpha particles passed through the foil with no deflection or with only a very small deflection.
What does this observation suggest about the atom?

Before the Geiger–Marsden experiment, the Thomson model described the atom as a sphere of positive charge spread evenly throughout its volume, with electrons embedded in it.
If this model were correct, what would be expected when alpha particles are fired at a thin gold foil?

Technetium-99m is used as a tracer in hospital bone scans. Its nucleus is represented as ⁹⁹₄₃Tc. How many neutrons does this nucleus contain?

Calcium in bone is present as Ca²⁺ ions. Consider a Ca²⁺ ion formed from an atom of ⁴⁰₂₀Ca. Which row gives the numbers of protons, neutrons and electrons in this ion?

A particle detector on a space probe identifies alpha particles in the solar wind. Compared with a neutral atom of ⁴₂He, an alpha particle

An electron in an atom moves from an energy level of −3.40 eV to an energy level of −13.6 eV.

Which row describes the photon involved in this transition?

The emission spectrum of a hot gas consists of bright lines. When white light passes through the same gas when it is cool, dark lines appear on a continuous spectrum at the same wavelengths as the bright lines.

What do these observations show?

Dark lines are seen in the spectrum of sunlight at wavelengths that match the bright lines of helium measured in a laboratory.

What can be concluded?

The ground state of an atom is at −13.6 eV. A photon of energy 15.0 eV is incident on an atom in its ground state.

Which row describes what happens?

The diagram shows three energy levels of an atom. Photon P is emitted in the transition from −0.85 eV to −3.40 eV and photon Q in the transition from −1.51 eV to −3.40 eV.

What is (wavelength of Q)/(wavelength of P)?

In the Geiger–Marsden–Rutherford experiment, alpha particles were directed at a thin gold foil.

Which row correctly links an observation to the conclusion drawn from it?

Light from the bright surface of the Sun has a continuous spectrum crossed by dark absorption lines. The dark lines are produced by a thin layer of cooler gas just above the surface. During a total eclipse the Moon hides the bright surface for a few seconds, and only light from this thin layer of gas, seen against the dark sky, enters a spectrometer.

What spectrum is observed during these few seconds?

A laser projector contains a red laser of wavelength 650 nm and a blue laser of wavelength 450 nm. Both lasers emit light with the same power.

What is (number of photons emitted per second by the red laser)/(number of photons emitted per second by the blue laser)?

The nucleus of a nuclide has a charge of +1.28 × 10⁻¹⁸ C and contains 18 nucleons.

Which is the nuclear notation for this nuclide? (X represents the chemical symbol.)

The diagram shows the path of an alpha particle that passes close to a single nucleus N in a thin metal foil. Q is the point on the path closest to N; P and R are points far from N.

Which row gives the point at which the speed of the alpha particle is least and the direction of the force on the alpha particle at that point?

In a Geiger–Marsden–Rutherford experiment, a narrow beam of alpha particles is directed at a thin metal foil in a vacuum, and the fraction of the alpha particles that are scattered through more than 90° is measured.

Which change, with everything else unchanged, increases this fraction?

Two discharge tubes contain chlorine atoms. One contains only ³⁵₁₇Cl and the other only ³⁷₁₇Cl. The two tubes produce line spectra that are almost identical.

What is the reason for this?

The diagram shows three energy levels of an atom, measured from the ground state. Atoms of a gas are excited to the 3.54 eV level and then return to the ground state.

What is the longest wavelength of the photons emitted?

A space telescope records the spectrum of a star. The spectrum is continuous but crossed by dark lines at specific wavelengths. Which statement best explains the dark lines?

Water purifiers use mercury lamps to produce ultraviolet light. In a mercury atom, the ground state has energy −10.4 eV and an excited state has energy −5.5 eV. What is the wavelength of the photon emitted when an electron falls from this excited state to the ground state?
(h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C)

An atom in a gas has a ground state of −5.0 eV, a first excited state of −2.6 eV and a second excited state of −1.4 eV. Two experiments are carried out on separate ground-state atoms: one is struck by a photon of energy 3.0 eV, and the other is struck by a free electron of kinetic energy 3.0 eV. Which statement is correct?

Visible light from a hot star passes through a cold cloud of hydrogen gas in interstellar space at about 20 K. The visible Balmer absorption lines of hydrogen, which involve transitions starting from n = 2, are almost absent from the spectrum. What is the best explanation?

Radiation with a continuous range of photon energies, from visible to far ultraviolet, passes through cold mercury vapour. Every atom in the vapour is in its ground state. In a simplified model, the only bound energy levels of mercury are −10.4 eV (ground state), −5.5 eV, −3.7 eV and −1.6 eV. Which photon energy will not be absorbed by the vapour?

Light from a hot tungsten filament passes through a glass cell containing cool sodium vapour. Observer P looks along the beam, straight through the cell. Observer Q looks at the cell from the side, at 90° to the beam, against a dark background. What do P and Q see when the light is passed through a spectrometer?

A forensic lab uses a gas-discharge lamp. Two of its spectral lines come from transitions with photon energies E₁ = 2.0 eV and E₂ = 3.0 eV. What is the ratio \(\frac{\lambda_1}{\lambda_2}\) of the wavelengths of these two lines?

Ultraviolet radiation of wavelength 60 nm from a hot young star ionizes ground-state hydrogen atoms in a nearby gas cloud. The ionization energy of hydrogen is 13.6 eV. What is the maximum kinetic energy of a freed electron?
(h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C)

Why was a very thin metal foil used in the Geiger–Marsden scattering experiment?

A semiconductor engineer uses alpha-particle backscattering to check silicon wafers for gold contamination. Per atom, gold impurity atoms send far more alpha particles back towards the detector than silicon atoms do.
Which property of gold is mainly responsible?

What is the main reason the alpha source, foil and detector in a Rutherford scattering experiment are placed inside an evacuated chamber?

Nuclear fuel is enriched by increasing the proportion of ²³⁵₉₂U relative to ²³⁸₉₂U. Chemical methods cannot separate the two. Enrichment in gas centrifuges is possible because atoms of the two isotopes have different

Caesium-137, ¹³⁷₅₅Cs, is a contaminant monitored after nuclear accidents. Which nuclide has the same number of neutrons as ¹³⁷₅₅Cs?

A study of corrosion in steel pipelines involves the iron isotope ⁵⁶₂₆Fe. Nucleus X has one fewer proton and three more neutrons than a ⁵⁶₂₆Fe nucleus. Which is the correct notation for X?

A nuclear submarine reactor uses fuel containing ²³⁵₉₂U. The unified atomic mass unit is 1.66 × 10⁻²⁷ kg. What is the approximate mass of one ²³⁵₉₂U nucleus?

A cyclotron used to produce medical isotopes can accelerate deuterons (²₁H nuclei) or alpha particles (⁴₂He nuclei). What is the approximate value of \(\frac{\text{charge-to-mass ratio of a deuteron}}{\text{charge-to-mass ratio of an alpha particle}}\)?

Some nuclear reactors use heavy water, D₂O, as a moderator. D is the isotope ²₁H and the oxygen is ¹⁶₈O. How many neutrons are there in one molecule of heavy water?

The diagram shows the four lowest energy levels of an atom. A cool gas of these atoms, all in the ground state, is illuminated with light containing a wide range of photon energies.

Which photon energy can be absorbed by the gas?

The diagram shows energy levels of an atom. An atom in the ground state absorbs a photon of energy 12.09 eV.

Which row gives the level to which the electron is raised and the number of different photon energies that can then be emitted as it returns to the ground state?

An atom in its ground state absorbs a photon of wavelength λ₁. The atom then returns to the ground state by emitting two photons in turn, of wavelengths λ₂ and λ₃, through one intermediate energy level.

What is λ₁?

Astronomers record the spectrum of a star while one of its planets passes in front of it, and again when the planet is not in front. Both spectra show the same set of dark lines, but while the planet is in front, extra dark lines appear at wavelengths of sodium. They disappear when the planet moves away.

What can be concluded?

The diagram shows the visible emission line spectra of three elements P, Q and R, and the emission spectrum of a sample of hot gas.

Which statement about the sample is correct?

The diagram shows four energy levels of an atom. In a hot gas of these atoms, some atoms are in each of the levels. Photons of visible light have energies from 1.8 eV to 3.1 eV.

How many lines in the emission spectrum of the gas are in the visible region?

In hydrogen, the shortest wavelength emitted in transitions ending on n = 1 is 91.2 nm. The energy levels are −13.6 eV for n = 1 and −3.40 eV for n = 2. What is the shortest wavelength emitted in transitions ending on n = 2?

Students use a computer simulation of the Geiger–Marsden–Rutherford experiment. Alpha particles, all with the same kinetic energy, are directed at a thin gold foil in a vacuum, and a detector counts the alpha particles scattered through an angle θ in 10.0 minutes. Like a real experiment, the simulation includes random variation; the uncertainty in a count N is ±√N.

A student builds a spectrometer from a smartphone camera, a narrow slit and a transmission diffraction film. The spectrum of a lamp falls across the camera sensor, and the position x of each bright line is read in pixels from the image. Each position has an uncertainty of ±2 pixels.

To calibrate the spectrometer the student uses a compact fluorescent lamp, whose line wavelengths are known. The table and the graph show the results. The student then views a hydrogen discharge tube, whose red line appears at x = 1238 pixels.

Energy levels of hydrogen: −13.6 eV, −3.40 eV, −1.51 eV, −0.85 eV. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

A student uses a calibrated spectrometer to measure the wavelengths of the seven brightest visible lines emitted by a gas-discharge tube whose label is missing. Each measured wavelength has an uncertainty of ±2 nm.

Measured wavelengths / nm: 446, 472, 493, 503, 589, 666, 707.

The table lists the brightest visible lines of four gases from a spectral database.

A student estimates the Planck constant using six light-emitting diodes (LEDs). For each LED the potential difference is increased slowly until the LED just begins to glow; this threshold p.d. V is read from a digital voltmeter (uncertainty ±0.05 V). The peak wavelength λ of each LED (uncertainty ±5 nm) is taken from the manufacturer's data sheet. The student assumes that the energy of each photon emitted equals eV.

(e = 1.60 × 10⁻¹⁹ C, c = 3.00 × 10⁸ m s⁻¹)

A student investigates the energy levels of argon with an electron-collision tube. Electrons leave a hot cathode and are accelerated through a potential difference V towards a wire grid in argon gas at low pressure. Beyond the grid, a small potential difference opposes the motion of the electrons towards a collector, and the current I at the collector is recorded as V is increased slowly.

The current falls sharply at a series of values of V. The value at which the n-th fall occurs is V_n; each value has an uncertainty of ±1.0 V because the minima are broad. The student's model is V_n = V₀ + nΔE/e, where ΔE is the energy needed to excite an argon atom from its ground state and V₀ is a constant. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

A single-photon detector produces one count for each photon that it detects. A student directs light of wavelength 785 nm from a laser diode through calibrated filters onto the detector, so that the power P reaching the detector is known, and records the count rate R. The uncertainty in each value of R is ±0.10 × 10⁶ s⁻¹. The fraction of the incident photons that the detector counts is its efficiency η.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹; 1 pW = 1.0 × 10⁻¹² W)

A gas-leak sensor uses a laser tuned to 1653.7 nm, a wavelength at which methane molecules absorb strongly. To test the sensor, a student fills a cell with air containing 1.0 % methane. Mirrors reflect the beam back and forth so that the path length L in the gas can be changed. The fraction T of the laser power transmitted is measured with an uncertainty of ±0.010. The measurement is repeated with the laser tuned to 1652.0 nm, where methane does not absorb.

The student's model is T = e^−kL, where k is a constant that is proportional to the concentration of methane.

A sodium lamp emits, among others, the four lines in the table. They were measured with three different spectrometers, for the ultraviolet, the visible and the infrared. A spectral database states that a sodium atom in one particular excited level can return to the ground state either by emitting the 330.2 nm photon, or by emitting the other three photons one after another. The table gives the photon energies E and their uncertainties ΔE.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

The cold, thin gas between the stars contains a small amount of sodium. Sodium atoms in their ground state absorb photons of wavelength 589.0 nm, so the spectrum of a distant star shows a narrow, dark interstellar sodium line at this wavelength.

A student takes from a database the stellar parallax angle p of eight hot stars that lie in almost the same direction in the sky, and the strength W of the interstellar sodium line in the spectrum of each star. The student assumes that W is proportional to the number of sodium atoms per unit area along the line of sight from the Earth to the star. Each value of W has an uncertainty of ±0.5 pm; the uncertainties in p are negligible. The graph shows W against the distance d of the star for six of the stars.

A student looks through a spectroscope at two light sources: a filament lamp and a discharge tube containing helium gas. Figure 1 shows the two spectra between 400 nm and 700 nm.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

A helium–neon laser contains a mixture of helium and neon gases in a glass tube. A potential difference across the tube accelerates electrons, which collide with helium atoms and excite them. Excited helium atoms then collide with neon atoms and excite them. The laser emits red light of wavelength 632.8 nm. The figure shows some energy levels of the two atoms.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C, m_e = 9.11 × 10⁻³¹ kg)

The colours of fireworks are produced by metal compounds that are heated strongly when a shell bursts. Lithium compounds give red light: lithium atoms emit visible lines at 610.4 nm and 670.8 nm. Sodium compounds give yellow light: sodium atoms emit visible light at 589.0 nm.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C, g = 9.81 m s⁻²)

Each pixel of a phone display contains red, green and blue organic light-emitting diodes (OLEDs). In each OLED, electrons passing through a thin layer of material move from a higher energy level to a lower one, and in each such transition one photon is emitted. The photons emitted by the green OLED have energy 2.33 eV and those emitted by the blue OLED have energy 2.66 eV. The red OLED emits light of wavelength 630 nm.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

Low-pressure sodium street lamps emit almost all of their light at a wavelength of 589 nm.
(h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C)

A low-pressure sodium lamp lights a car park. Almost all of its visible output is at a wavelength of 589 nm, and the lamp emits 35 W of light at this wavelength.
(h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹)

A science centre builds an interactive exhibit that simulates the Geiger–Marsden experiment. On screen, alpha particles are fired at a thin foil of gold-197, \(^{197}_{79}\text{Au}\).

Cobalt-60, ⁶⁰₂₇Co, has been used as a gamma-ray source in radiotherapy machines for treating tumours.
Elementary charge e = 1.60 × 10⁻¹⁹ C.

A sample of magnesium from a meteorite is analysed. The table gives the stable isotopes found.

Nuclide | Relative abundance / % | Atomic mass / u
²⁴₁₂Mg | 79.0 | 23.985
²⁵₁₂Mg | 10.0 | 24.986
²⁶₁₂Mg | 11.0 | 25.983

In an experiment of the Geiger–Marsden–Rutherford type, a narrow beam of alpha particles, all with the same kinetic energy, is directed at a very thin gold foil, ¹⁹⁷₇₉Au, inside an evacuated chamber. A detector that can be moved around the foil counts the alpha particles scattered through different angles.

Figure 1 shows three alpha particles, P, Q and R, approaching one gold nucleus. R is moving directly towards the nucleus.

Figure 1 shows four energy levels, E₁ to E₄, of the atoms of an element Q. E₁ is the ground state.

When Q is very hot it emits a line spectrum. In the visible region, 400 nm to 700 nm, there are three lines, at 478 nm, 497 nm and 654 nm (Figure 2, upper strip).

In a second experiment, white light is passed through a tube of Q vapour at room temperature and the transmitted light is examined with a spectroscope. The lower strip of Figure 2 shows the spectrum of the white light before it enters the tube.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)