E.1 Structure of the atom

Hydrogen atoms are excited to the n = 4 energy level.

What is the maximum number of different spectral lines that can be emitted as the atoms return to the ground state?

The spectrum of a distant star shows two dark lines at 589.0 nm and 589.6 nm. A sodium lamp in the laboratory emits bright lines at exactly these wavelengths.

What is the best explanation of the dark lines?

A nucleus P contains 19 protons and 21 neutrons. In the options, X stands for the chemical symbol of whichever element the nucleus belongs to.

Which nucleus is an isotope of P?

The diagram shows the emission line spectra of three elements P, Q and R, and the emission spectrum of a gas-discharge lamp. Every line in each element's spectrum in this wavelength range is shown.

Which elements are present in the lamp?
I. P
II. Q
III. R

A hydrogen lamp is used to calibrate a spectrometer on a space telescope. In the lamp, hydrogen atoms are excited to the n = 5 energy level and no higher. The atoms then return to the ground state by every possible route. How many different wavelengths can be emitted?

Four energy levels of hydrogen are −13.6 eV (n = 1), −3.40 eV (n = 2), −1.51 eV (n = 3) and −0.85 eV (n = 4). Which transition emits the photon with the longest wavelength?

In a scattering experiment, a beam of alpha particles is directed at a thin gold foil. Almost all of the alpha particles pass through the foil with little or no deflection. What does this observation alone suggest about the atom?

Why must the metal foil in an alpha-particle scattering experiment be extremely thin?

An alpha particle moves directly towards a heavy nucleus. The nucleus remains stationary.
Which statement is correct at the instant the alpha particle is at its distance of closest approach?

In a fluorescent lamp the mercury vapour emits mostly ultraviolet photons. The coating on the inside of the glass tube emits visible light. Which statement best explains how the coating produces visible light?

White light passes through a cool sample of hydrogen gas and is then analysed with a spectrometer. The spectrum shows dark lines on a bright continuous background. What is the origin of the dark lines?

Which statement best explains why the emission spectrum of a hot, low-density gas consists of discrete bright lines?

White light passes through a cool gas and is then analysed with a spectrometer, which shows dark lines at certain wavelengths. What is the best explanation of the dark lines?

In Rutherford's alpha-particle scattering experiment a very small fraction of the alpha particles was deflected through angles greater than 90°. Which conclusion does this observation support?

In a scattering experiment, a narrow beam of α particles is directed at a very thin gold foil. A very small fraction of the α particles is deflected through angles greater than 90°. What can be deduced from this observation?

White light from a filament lamp passes through cool sodium vapour and is then analysed with a spectrometer. Which statement describes the spectrum that is seen?

A red LED in an optical communications link emits light of wavelength 620 nm. Use h = 6.63 × 10⁻³⁴ J s and c = 3.00 × 10⁸ m s⁻¹. What is the energy of one photon of this light?

A cool gas contains hydrogen atoms that are all in the ground state. The energy levels of hydrogen are given by E = −13.6/n² eV.

Photons of three different energies pass through the gas:
I. 10.2 eV
II. 11.0 eV
III. 14.0 eV

Which photons can be absorbed by the hydrogen atoms?

In the Bohr model of hydrogen, the electron's angular momentum is nh/2π and its orbital radius is proportional to n².

What is the ratio (speed of the electron in n = 2) / (speed in n = 1)?

Nucleus X has nucleon number 27 and nucleus Y has nucleon number 216.

Which row is correct?

The diagram shows some energy levels of hydrogen and four transitions A, B, C and D in which photons are emitted.

Which transition produces the photon of longest wavelength?

Alpha particles are scattered by a thin foil. For alpha-particle kinetic energies below about 25 MeV the number scattered through large angles agrees with the Rutherford model, which assumes only an electric repulsion between the alpha particle and a point nucleus. At higher kinetic energies fewer alpha particles are scattered through large angles than the model predicts.

Which conclusion is best supported by these observations?

In a Geiger–Marsden–Rutherford type experiment, a narrow beam of alpha particles is directed at a thin metal foil in a vacuum, and the number of alpha particles scattered through angles greater than 90° in a fixed time is counted.

Which change, made on its own, increases this number?

In the Bohr model of hydrogen, the angular momentum of the electron is mvr = nh/2π and the energy levels are E = −13.6/n² eV.

The electron is in an orbit in which its angular momentum is L. What is the minimum energy needed to ionise the atom from this state?

In the Bohr model of hydrogen, the electron moves from the n = 1 orbit to the n = 3 orbit. By what factors do the orbital radius and the orbital speed of the electron change?

Beams of the ion ⁴⁸₂₀Ca²⁺ are used in accelerators to make superheavy elements. What are the numbers of protons, neutrons and electrons in one of these ions?

In a scattering experiment, alpha particles approach a heavy nucleus head-on. The initial kinetic energy of the alpha particles is doubled. Recoil of the nucleus can be ignored. What happens to the distance of closest approach?

When an exoplanet passes in front of its star, some starlight passes through the planet's cool atmosphere before reaching a telescope. Sodium vapour is present in the atmosphere. Which statement about the observed spectrum is correct?

Nucleus P has a nucleon number 27 times that of nucleus Q. Which row gives the ratio \(\frac{\text{radius of P}}{\text{radius of Q}}\) and the ratio \(\frac{\text{density of P}}{\text{density of Q}}\)?

An alpha particle with kinetic energy E is fired head-on at a stationary gold nucleus. Its distance of closest approach is d. A proton, also with kinetic energy E, is then fired head-on at the same nucleus. Recoil of the nucleus is negligible. What is the distance of closest approach of the proton?

An atom used in a laboratory gas-discharge lamp has only four energy levels: −9.0 eV, −4.0 eV, −2.0 eV and −0.5 eV. Which photon energy can not be emitted by this atom?

A space telescope observes a hot star through a cool cloud of interstellar gas. Which best describes the spectrum of the light that reaches the telescope?

Hydrogen energy levels are given by E_n = −13.6/n² eV. An astronomer compares photon X, emitted in the transition n = 3 → n = 2, with photon Y, emitted in the transition n = 2 → n = 1. What is \(\frac{\text{wavelength of X}}{\text{wavelength of Y}}\)?

Radio telescopes detect hydrogen atoms in interstellar space with electrons in extremely high levels. Using the Bohr model, E_n = −13.6/n² eV, what is the ionization energy of a hydrogen atom with n = 100?

An alpha particle with kinetic energy E travels directly towards a stationary nucleus. Its distance of closest approach is d.
A proton with the same kinetic energy E travels directly towards an identical stationary nucleus. What is the proton's distance of closest approach?

Nucleus P has nucleon number 8. Nucleus Q has nucleon number 125.
What is the value of \(\frac{\text{radius of Q}}{\text{radius of P}}\)?

When alpha particles of very high kinetic energy are scattered by nuclei, the number scattered through large angles is less than the Rutherford model predicts.
What is the best explanation?

A lamp used for greenhouse lighting contains a vapour whose atoms have these four energy levels: −8.0 eV, −3.0 eV, −1.5 eV and −0.5 eV. Atoms in the n = 4 level (−0.5 eV) make transitions to lower levels. Which transition produces the photon of longest wavelength?

A sample of gas has atoms that can occupy only the levels n = 1, 2, 3 and 4, with all energy gaps different. Atoms are excited to n = 4. What is the maximum number of different photon energies that can be emitted as the atoms return to the ground state?

The energy levels of hydrogen are given by E_n = −13.6/n² eV. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed. A hydrogen atom makes a transition from n = 2 to n = 1. What is the wavelength of the emitted photon?

Sodium vapour lamps on an airport apron emit strongly at a wavelength of 589 nm. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed. What is the energy difference between the two atomic levels involved in this emission?

An alpha particle of kinetic energy 6.0 MeV is fired directly at the nucleus of an aluminium atom (atomic number 13). Ignoring recoil of the nucleus, what is the distance of closest approach? (k = 8.99×10⁹ N m² C⁻², e = 1.60×10⁻¹⁹ C)

The nuclear radius is given by R = R₀A^1/3. What is the approximate ratio of the radius of a uranium-238 nucleus to the radius of a helium-4 nucleus?

A proton and an alpha particle, each with the same kinetic energy, are fired directly at the same stationary heavy nucleus. Ignoring recoil, what is (closest approach of the alpha particle) ÷ (closest approach of the proton)?

Light of wavelength 656 nm is incident normally on a diffraction grating with 500 lines per millimetre. What is the angle between the two first-order maxima, one on each side of the central maximum?

In the Bohr model of the hydrogen atom, what is the orbital angular momentum of the electron when it is in the n = 2 energy level? (h is the Planck constant.)

The atoms of a gas in a discharge lamp have only four energy levels, at −5.0 eV, −3.1 eV, −1.6 eV and −0.8 eV. Atoms excited to the −0.8 eV level can return to lower levels by any sequence of downward transitions. What is the maximum number of different photon energies in the emission spectrum of the gas?

An atom has three energy levels E₁ < E₂ < E₃. The transition from E₃ to E₁ emits a photon of wavelength λ₃₁ and the transition from E₂ to E₁ emits a photon of wavelength λ₂₁.

What is the wavelength of the photon emitted in the transition from E₃ to E₂?

In the Bohr model of hydrogen the radius of the orbit with quantum number n is n²r₁, where r₁ is the radius of the smallest orbit, and the angular momentum of the electron is mvr = nh/2π.

What is the de Broglie wavelength of the electron in the orbit with quantum number n?

An alpha particle of kinetic energy E is directed head-on at a nucleus and reaches a distance of closest approach d. A proton of kinetic energy E/2 is then directed head-on at the same nucleus. The nucleus remains at rest in both cases.

What is the distance of closest approach of the proton?

Alpha particles are fired head-on at nuclei. In a simple model, deviations from Rutherford scattering begin at the kinetic energy E_dev for which the distance of closest approach equals the nuclear radius R = R₀A^1/3.

Gold has Z = 79 and A = 197; aluminium has Z = 13 and A = 27. What is E_dev(gold)/E_dev(aluminium)?

In the Bohr model, the energy levels of a one-electron ion with proton number Z are E_n = −13.6 Z²/n² eV. Singly ionised helium, He⁺ (Z = 2), emits a photon in the transition n = 4 → n = 2. Which transition in hydrogen emits a photon of the same wavelength?

In the Bohr model, the electron's orbit can be pictured as a whole number of de Broglie wavelengths fitting around the circumference. How does the de Broglie wavelength of the electron in the n = 3 orbit of hydrogen compare with its value in the n = 1 orbit?

In the Bohr model of hydrogen, the electron moves from the n = 2 orbit to the n = 4 orbit. What is \(\frac{\text{de Broglie wavelength in } n=4}{\text{de Broglie wavelength in } n=2}\)?

The hydrogen energy levels are E_n = −13.6/n² eV. What is \(\frac{\text{longest wavelength in the Lyman series}}{\text{longest wavelength in the Balmer series}}\)?

In the Bohr model of hydrogen, the orbital radius is proportional to n² and the electron's orbital speed is proportional to 1/n. What is \(\frac{\text{orbital period in } n=2}{\text{orbital period in } n=1}\)?

Nucleus X has nucleon number A. Nucleus Y has nucleon number 8A.
Which row gives the ratio of radius and the ratio of nuclear density, Y : X?

Alpha particles with the same initial kinetic energy are directed head-on at a gold nucleus, ¹⁹⁷₇₉Au, and at an aluminium nucleus, ²⁷₁₃Al. Treat each nucleus as a stationary point charge that does not recoil. What is \(\frac{\text{distance of closest approach to gold}}{\text{distance of closest approach to aluminium}}\)?

Muonic hydrogen consists of a proton and a negative muon. The muon has the same charge as an electron and a mass about 207 times as great. Using the Bohr model with the proton assumed to be stationary, how do the ground-state orbital radius and the magnitude of the ground-state energy of muonic hydrogen compare with those of ordinary hydrogen?

In the Bohr model of hydrogen, the electron orbit radius is proportional to n², and the electron's angular momentum is nh/2π. How does the orbital speed of the electron in the n = 3 orbit compare with its speed in the n = 1 orbit?

An α particle with kinetic energy E is fired directly at a stationary nucleus of charge +Ze. It stops momentarily at a distance r₀ from the centre of the nucleus. A proton with the same kinetic energy E is fired directly at a stationary nucleus of charge +2Ze. Ignore any motion of the nuclei. What is the closest approach of the proton to the centre of its target nucleus?

Beams of high-energy electrons are scattered by thin targets of six different elements. From the angle of the first minimum of each diffraction pattern, the radius R of the target nuclei is deduced. A student wishes to test the hypothesis that R = R₀Aⁿ, where A is the nucleon number and R₀ and n are constants, and so plots ln(R / fm) against ln A. The graph shows the data and the line of best fit, which has been drawn only across the range of the data.

(1 fm = 1.0 × 10⁻¹⁵ m; 1 u = 1.66 × 10⁻²⁷ kg)

A beam of alpha particles, all with the same kinetic energy, is directed in turn at thin foils of six different metals in an evacuated chamber. Every foil contains the same number of atoms per unit area. A detector at a fixed scattering angle counts the number N of alpha particles that arrive in 30 minutes. Background counts are negligible. Rutherford's model predicts that N ∝ Z², where Z is the proton number of the nuclei in the foil.

The graph shows ln N against ln Z with the line of best fit. The error bars show the random uncertainty ±√N in each count.

In a teaching version of the Geiger–Marsden–Rutherford experiment, a narrow beam of alpha particles strikes a thin gold foil in an evacuated chamber. A detector on a rotating arm counts the alpha particles N arriving in 20 minutes at each angle reading θ on the arm's scale. Before the foil was inserted, the student found that the unscattered beam gave its maximum count at a scale reading of +2.0°. Rutherford's model predicts N = k(sin(θ/2))⁻ⁿ with n = 4, where k is a constant.

The graph shows ln N against ln(sin(θ/2)), calculated from the scale readings, with the line of best fit.

In a tube containing sodium vapour at low pressure, electrons from a hot cathode are accelerated from rest through a variable potential difference V towards a wire grid. Electrons that pass the grid must overcome a small retarding potential difference to reach a collecting plate. As V is increased, the collector current rises and falls repeatedly, because an electron that has gained exactly enough energy can give the first excitation energy E of a sodium atom to an atom in an inelastic collision.

A simple model predicts that the k-th current maximum occurs at V_k = kE/e. The table gives V at the first six maxima; each value is uncertain by ±0.10 V. The graph shows V against k with the line of best fit, extended to k = 0. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

Light from a hydrogen discharge tube is passed through a diffraction grating with 600 lines per mm mounted on a spectrometer. The student measures the first-order angle of diffraction θ for five visible lines, each produced by a transition from an upper level n to the same lower level n_f. Modelling the energy levels as E_n = −E_I/n², she predicts that 1/λ = (E_I/hc)(1/n_f² − 1/n²) and plots 1/λ against 1/n².

The graph shows four of the points with the line of best fit. (h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C)

Iodine-131, ¹³¹₅₃I, is used in medicine to treat thyroid conditions. The stable form of iodine found in food is iodine-127.

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.

Household smoke detectors contain americium-241, which emits alpha particles with kinetic energy 5.49 MeV. A student considers one of these alpha particles travelling directly towards a tin nucleus, \(^{120}_{50}\text{Sn}\), in the solder of the detector's circuit board. Assume the tin nucleus stays at rest.
k = 8.99×10⁹ N m² C⁻², e = 1.60×10⁻¹⁹ C.

In a fluorescent lamp, a low-pressure mercury vapour is excited by electrons that travel along the tube. The excited mercury atoms emit ultraviolet radiation of wavelength 254 nm. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed.

A research greenhouse uses a vapour lamp. Atoms in the vapour have the following energy levels.
n = 1: −10.0 eV; n = 2: −4.5 eV; n = 3: −2.0 eV; n = 4: −1.0 eV. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed.

Aircraft obstruction beacons on a hill use neon lamps that emit red light of wavelength 640 nm. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed.

A mercury-vapour lamp is used to disinfect a water supply. One strong emission line from the vapour has wavelength 254 nm. h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C.

In a pharmacy laboratory the sodium content of a rehydration solution is checked using atomic absorption. A vapourised sample is illuminated with white light and the transmitted light shows a dark line at 589 nm. h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C.

Light from a hydrogen discharge tube is incident normally on a diffraction grating that has 600 lines per millimetre. The diagram shows some of the energy levels of the hydrogen atom, E_n = −13.6/n² eV.

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

In a fluorescent lamp, electrons accelerated by an electric field collide with atoms in low-pressure mercury vapour. The diagram shows some of the energy levels of the mercury atom.

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

Hydrogen atoms in a stellar atmosphere are modelled using the Bohr model. The radius of the ground-state orbit is 5.29 × 10⁻¹¹ m. Consider an electron in the n = 3 orbit.
Electron mass = 9.11 × 10⁻³¹ kg; h = 6.63 × 10⁻³⁴ J s.

An engineer is choosing a gas for a new display lamp. The four lowest energy levels of the gas atoms are given in the table.

Level | Energy / eV
E₁ | −9.80
E₂ | −5.10
E₃ | −3.20
E₄ | −1.40

Visible light has photon energies from 1.77 eV to 3.10 eV.

A solar telescope uses a narrow filter centred on the hydrogen-alpha line at 656 nm to image the Sun's outer layers. The energy levels of hydrogen are E_n = −13.6/n² eV.
h = 6.63 × 10⁻³⁴ J s; c = 3.00 × 10⁸ m s⁻¹; e = 1.60 × 10⁻¹⁹ C.

A neutron star can be roughly modelled as a single giant nucleus with the same density as ordinary nuclear matter. Nuclear radius is R = R₀A^1/3, with R₀ = 1.20 × 10⁻¹⁵ m. The mass of a nucleon is 1.67 × 10⁻²⁷ kg.

A gas X is being tested for use in a new ultraviolet sterilisation lamp. Its lowest four energy levels are:
n = 1 (ground state): −8.20 eV
n = 2: −4.10 eV
n = 3: −2.60 eV
n = 4: −1.30 eV
Use h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C.

Images of star-forming nebulae are often taken through filters that pass the red H-alpha line of hydrogen. The hydrogen energy levels are E_n = −13.6/n² eV.
h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C.

In a laboratory plasma experiment, some hydrogen atoms are in excited states. Infrared light of wavelength 1064 nm from a Nd:YAG laser, of the kind used in surgery, is shone on the gas. The Bohr model gives the energy levels of hydrogen as E_n = −13.6/n² eV.
(h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C)

Engineers designing a small ion-beam facility want to know the minimum kinetic energy an alpha particle needs to just make contact with a lead-208 nucleus, \(^{208}_{82}\text{Pb}\), in a head-on approach. Treat both the alpha particle and the lead nucleus as spheres. Contact occurs when the separation of their centres equals the sum of their radii. Assume the lead nucleus does not recoil.
R₀ = 1.20 fm, k = 8.99×10⁹ N m² C⁻², e = 1.60×10⁻¹⁹ C, 1 MeV = 1.60×10⁻¹³ J.

Fuel rods for nuclear power stations contain mostly ²³⁸₉₂U. The radius R of a nucleus of nucleon number A is given by R = R₀A^1/3, where R₀ = 1.20 × 10⁻¹⁵ m.
1 u = 1.661 × 10⁻²⁷ kg.

A technician at a concert hall tests a hydrogen discharge tube for a lighting demonstration. The energy levels of hydrogen are given by \(E_n=-\frac{13.6}{n^2}\) eV. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed.

An airborne instrument passes light from a lamp that emits all visible wavelengths through a cell of cool hydrogen gas. The transmitted light is analysed and dark lines are seen at certain wavelengths. The energy levels of hydrogen are given by \(E_n=-\frac{13.6}{n^2}\) eV. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed.

In the Bohr model of hydrogen, the radius of the nth orbit is \(r_n=n^2r_1\), where \(r_1=5.29\times10^{-11}\) m, and the angular momentum of the electron is \(\frac{nh}{2\pi}\). Consider the electron in the n = 3 orbit. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C (1 eV = 1.60 × 10⁻¹⁹ J) and m_e = 9.11 × 10⁻³¹ kg where needed.

Alpha particles of kinetic energy 7.7 MeV are directed head-on at a thin gold foil. A gold nucleus has atomic number 79 and mass number 197. Ignore recoil of the nucleus. k = 8.99×10⁹ N m² C⁻², e = 1.60×10⁻¹⁹ C; the nuclear radius is R = R₀A^1/3 with R₀ = 1.20×10⁻¹⁵ m.

A copper nucleus has mass number 64 and atomic number 29. In a scattering experiment alpha particles are fired head-on at copper nuclei. k = 8.99×10⁹ N m² C⁻², e = 1.60×10⁻¹⁹ C; R₀ = 1.20×10⁻¹⁵ m.

In a physics simulation game, the player must identify an unknown nucleus. An alpha particle of kinetic energy 6.50 MeV is fired head-on at the nucleus and the game reports a distance of closest approach of 2.21×10⁻¹⁴ m. The game ignores recoil. k = 8.99×10⁹ N m² C⁻², e = 1.60×10⁻¹⁹ C.

In the Bohr model of hydrogen the energy of level n is −13.6/n² eV, the orbital radius is n²r₁ with r₁ = 5.29×10⁻¹¹ m, and the angular momentum of the electron is nh/2π. h = 6.63×10⁻³⁴ J s, c = 3.00×10⁸ m s⁻¹, e = 1.60×10⁻¹⁹ C; electron mass 9.11×10⁻³¹ kg.

A food scientist heats three samples of seasoning in a flame and examines the light with a spectrometer. Reference lines for four elements are shown. Each element is identified here by the single line listed.

Sodium: 589 nm
Potassium: 767 nm
Lithium: 671 nm
Barium: 554 nm

One sample produces lines at 554 nm, 589 nm and 767 nm. Use h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹ and 1 eV = 1.60 × 10⁻¹⁹ J.