Energy levels & line spectra

In 1864, William Huggins and William Miller used dark lines in the spectrum of the Sun to identify elements in the Sun’s atmosphere.

*(a) Explain how gases in the Sun’s atmosphere cause dark lines in the spectrum corresponding to different elements.

In 1868, William Huggins analysed light from the star Sirius A. The wavelength of the hydrogen-alpha line for light from Sirius A was slightly different from the hydrogen-alpha line observed from a source in a laboratory.

Huggins suggested that this difference could be explained using the Doppler effect and could be used to determine the speed and direction of the star’s motion relative to the Earth.

Assess Huggins’s suggestion.

Sirius A has a component of velocity away from the Earth of 5.5 km s^–1.

The wavelength of the hydrogen-alpha line observed from a source in the laboratory is 656.46 nm.

Calculate the wavelength of the hydrogen-alpha line as seen in the spectrum of Sirius A.

Scientists can analyse light from stars that has passed through a diffraction grating.

*(a) Explain the pattern produced when a mixture of blue and red light, from the same source, passes through a diffraction grating.

Light interacts with atoms as it passes through the atmosphere of the star.

Explain how this leads to the formation of the dark lines within the spectrum.

The surface temperature of the star is 5800 K.

On the axes below, sketch a graph of the intensity of radiation against the wavelength of that radiation for this star.

This star is a main sequence star.

Explain why main sequence stars do not collapse due to gravitational forces.

The neon lamp shown is a glass bulb filled with neon gas at low pressure.

(Source: https://media.digikey.com/Photos/Visual%20Communications%20Company%20VCC/ A1A.JPG)

*(a) When in use, the neon gas between the electrodes emits electromagnetic radiation.

Explain why this happens when there is an electric current between the electrodes.

When light from the neon lamp is incident upon a metal surface, electrons with a maximum speed of 2.68 10⁵m s⁻¹ are emitted from the surface.

The table shows the work functions of some metals.

Deduce which metal the light is incident upon.

frequency of light from the neon lamp = 5.56 × 10¹⁴Hz

A fine-beam tube is used for investigating properties of electrons.

An electron beam is produced inside a spherical glass bulb. The bulb contains neon gas at a very low pressure.

The neon gas is at a pressure of 1.25 Pa and a temperature of 25 °C.

Calculate the number N of neon atoms inside the bulb.

bulb diameter = 16.0 cm

*(b) Interactions between electrons and the neon atoms in the tube make the beam visible. Part of the spectrum of visible light produced by these interactions is shown.

Explain the process that results in the emission of this spectrum. Your answer should include reference to energy levels in atoms.

In 1905 Einstein published his equation for the photoelectric effect.

In 1916 Millikan demonstrated that the maximum kinetic energy of photoelectrons is consistent with Einstein’s equation.

*(a) Discuss the extent to which our current understanding of observations of the photoelectric effect supports the idea that light behaves as photons rather than as waves.

Millikan used his data to obtain a value of the Planck constant.

The following graph of maximum kinetic energy of photoelectrons against frequency was produced from his data for the photoelectric effect using lithium.

Millikan suggested that the uncertainty from his results for lithium was as little as 1%.

Determine whether the value of the Planck constant obtained from this graph is within 1% of the value stated on the data sheet for this examination paper.

Millikan used a device known as a monochromator to ensure that a single wavelength of light was used to illuminate the surface of the lithium. A monochromator separates wavelengths using a diffraction grating.

Calculate the angle at which a diffraction grating would produce the most intense line at a single wavelength of 6.1 × 10⁻⁷m.

number of lines per mm for grating = 600 mm⁻¹

In 1905 Einstein published his equation for the photoelectric effect.

In 1916 Millikan demonstrated that the maximum kinetic energy of photoelectrons is consistent with Einstein’s equation.

*(a) Discuss the extent to which our current understanding of observations of the photoelectric effect supports the idea that light behaves as photons rather than as waves.

Millikan used his data to obtain a value of the Planck constant.

The following graph of maximum kinetic energy of photoelectrons against frequency was produced from his data for the photoelectric effect using lithium.

Millikan suggested that the uncertainty from his results for lithium was as little as 1%.

Determine whether the value of the Planck constant obtained from this graph is within 1% of the value stated on the data sheet for this examination paper.

Millikan used a device known as a monochromator to ensure that a single wavelength of light was used to illuminate the surface of the lithium. A monochromator separates wavelengths using a diffraction grating.

Calculate the angle at which a diffraction grating would produce the most intense line at a single wavelength of 6.1 × 10⁻⁷m.

number of lines per mm for grating = 600 mm⁻¹

After the light passes through the diffraction grating a line spectrum is observed.

Our understanding of the atom has developed over time, from early models in which atoms were considered to be hard incompressible spheres, through to the nuclear model of the atom and the ladder model in which electrons exist in a discrete number of allowed energy states.

*(a) The model of atoms as hard incompressible spheres, moving rapidly and randomly, can be used to explain why gases exert a pressure.

Explain, using ideas of momentum, why the pressure exerted by a gas increases as the temperature of the gas increases.

The nuclear model of the atom was established following a series of experiments in which alpha particles were directed at thin gold foil.

An alpha particle approaching a gold nucleus,¹⁹⁷₇₉Au, head-on will be brought to rest and returned along its original path.

Calculate the minimum distance between the alpha particle and the nucleus for alpha particles of energy of 5.5 MeV.

It is observed that electrons, with energy of 5.5 keV, are diffracted as they pass through the thin gold foil.

Explain a conclusion about the electrons that can be made from this observation.

In the energy ladder model of the atom, electrons exist in a discrete number of allowed energy states. The collision of electrons with gold atoms may lead to the production of high frequency electromagnetic radiation.

Explain how high frequency electromagnetic radiation may be produced when electrons collide with atoms in a metal.

Barnard’s star is a red dwarf star in the vicinity of the Sun. The wavelength of a line in the spectrum of light emitted from Barnard’s star is measured to be 656.0 nm. The same light produced by a source in a laboratory has a wavelength of 656.2 nm.

Calculate the velocity of Barnard’s star relative to the Earth.

A diffraction grating can be used to analyse the radiation emitted by a variety of sources.

A diffraction grating of known grating spacing is used in a school laboratory to analyse the light emitted by a laser.

Describe how the diffraction grating is used and the measurements that should be taken.

A diffraction grating with grating spacing of 2.2 × 10⁻⁶ m is used to determine the difference in wavelength for the spectral line emitted by Barnard’s star.

Comment on the suitability of using a diffraction grating with this spacing. You should include appropriate calculations.

Visible light from the star originates from the photosphere. In the photosphere of Barnard’s star, hydrogen and helium atoms are at a temperature of 3100 K.

Calculate the mean kinetic energy of an atom in the photosphere at a temperature of 3100 K.

Describe how these atoms emit visible light.