Diffraction gratings

A student shone green light from a laser through a diffraction grating, producing a diffraction pattern on a screen. The student determined the angle of the third order maximum.

Calculate the wavelength of the green light.

angle of third order maximum = 73.3° grating spacing = 1.67 × 10^–6m

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.

A student used a laser pointer to direct monochromatic light normal to the plane of a diffraction grating as shown.

A diffraction pattern was produced on the screen. The distance between the first order maximum and the central maximum of the diffraction pattern was x. The distance between the diffraction grating and the screen was D.

The diffraction grating had 300 lines per mm. The laser pen was marked with λ = 520 nm.

Determine whether the spacing of the diffraction pattern was consistent with these values.

x = 43.5 cm D = 2.75 m

The student wrote the following conclusion:

“The value of x was measured with a metre rule. A metre rule has a precision of 0.1 cm, so this value was determined with a high degree of accuracy.”

Comment on this conclusion.

Light from a laser pointer was passed through a diffraction grating. The light was perpendicular to the diffraction grating as shown. A diffraction pattern was produced on

The distance between the first order maximum and the central maximum of the diffraction pattern was x. The distance between the diffraction grating and the screen was D.

Distance x was measured to be 0.500 m with a metre rule. The wavelength of light λ₁ from the laser pointer was 650 nm. The laser pointer was replaced with one that produced light of a different wavelength. The new distance x was measured to be 0.400 m.

D = 1.45 m

Calculate the wavelength λ₂ of the light emitted by the replacement laser pointer.

Explain one modification to this method that would decrease the uncertainty in the

In another experiment, the light from the laser pointer was not quite perpendicular to the screen.

Explain how this would change the diffraction pattern produced on the screen.

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.

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.