E.1 Structure of the atom: IB Physics SL exam-style questions

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 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?

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 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?

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?

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?

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.

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.

In a gas-discharge lamp, electrons are accelerated by a potential difference and then collide with atoms of a gas. A collision can transfer energy from an electron to an atom and excite the atom.

The figure shows the four lowest energy levels, E₁ to E₄, of an atom of the gas. Before a collision every atom is in the ground state E₁. Ignore the kinetic energy given to the atom as a whole in a collision.

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

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)

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?

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 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?

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?

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)

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.

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)

The spectrum of a star S shows dark absorption lines on a continuous background. Table 1 gives the wavelengths of the absorption lines of S. Table 2 gives laboratory wavelengths of some lines of four elements.

(c = 3.00 × 10⁸ m s⁻¹, Wien's displacement constant = 2.9 × 10⁻³ m K)

Copper has two stable isotopes, copper-63 and copper-65. In a mass spectrometer, copper atoms are ionized so that every ion carries a charge of +e. The ions pass through a velocity selector and then through a narrow slit S into a region of uniform magnetic field of flux density 0.400 T directed into the page, where they move in semicircles and strike a detector plate (Figure 1).

In the velocity selector the ions move between two parallel plates 2.00 cm apart with a potential difference of 640 V between them. A uniform magnetic field of flux density 0.160 T, perpendicular to both the electric field and the velocity of the ions, also acts in the selector.

Masses of the ions: ⁶³Cu⁺ 62.93 u, ⁶⁵Cu⁺ 64.93 u. (1 u = 1.661 × 10⁻²⁷ kg, e = 1.60 × 10⁻¹⁹ C)

In a fluorescent lamp, mercury atoms emit ultraviolet photons of wavelength 254 nm. The inside of the glass tube is coated with a phosphor, which absorbs these photons and emits visible light.

The diagram shows four energy levels of an ion in the phosphor. The energies are measured from the ground state.

(h = 6.63 × 10⁻³⁴ J s, c = 3.00 × 10⁸ m s⁻¹, e = 1.60 × 10⁻¹⁹ C, Wien's displacement constant = 2.90 × 10⁻³ m K)