H557/02 Scientific literacy in physics OCR B Advancing Physics
Questions on the advance notice article
Introduction
Q1. What type of scale is shown in Figure 1?[1]
Q2. Give an advantage of the type of scale shown in Figure 1.[1]
Q3. Give a disadvantage of the type scale shown in Figure 1.[1]
Q4. Using the scale in Figure 1, estimate the volume and the mass of a flea, stating any assumptions that you make. [3]
The world of the very small – angular resolution of optical images
Q1. An equation that gives an approximation for the angular resolution of an optical system is:
angular resolution (radians) =
Explain the origin of this equation by consideration of the diffraction of light from two closely-spaced sources when the light passes through the aperture. [3](Hint: review diffraction work of Chapter 6 and research online)
Q2. Determine the angular resolution of the human eye, in radians and degrees, when viewing an object emitting red light of wavelength 600 nm. Assume the diameter of the pupil, which determines the aperture, is 3 mm. [3]
Q3. How closely spaced could two objects be if they are just resolvable with the human eye at a distance of 100 m. Use the angular resolution calculated in the previous question. [2]
Q4. How closely spaced could two stars be in a cluster of stars 30 light years away if they are just resolvable with the naked eye? [2]
Q5. Research the density and molar mass of the element iron and use it to determine the volume occupied by an iron atom and hence estimate the diameter of an iron atom. Take NA = 6.02 x 1023 mol-1. [4]
The distance to the nearest stars
Q1. Draw a labelled diagram and use it to demonstrate that the distance to a star from the Sun is given by:
d =,
whereL is the Earth-Sun baseline distance and p the parallax angle.[3]
Q2. Explain why it does not much matter whether we specify the distance to the star from the Earth or from the Sun. [2]
Q3. (a) Use Bessel’s parallax angle to estimate the distance to 61 Cygni in metres. Take the Earth-Sun distance as 150 x 106 km. [1]
Q3. (b) Convert the value you obtained in the previous question to light years.[2]
Q4. Explain why diffraction of light entering a telescope will limit the measurement of small parallax angles. [2]
Q5. Give reasons why reflecting telescopes (objective mirror) are more suited to parallax measurements than refracting telescopes (objective lens). [2]
The astronomical unit and the parsec
Q1. Use the parallax equation derived earlier to show that 1 parsec is approximately 3.1 x 1016 m. [1]
Q2. Explain why, for small angles[2]
distance in parsecs =
Q3. What is the distance in parsecs to a star whose parallax angle is 0.05 arc seconds?[1]
Gaia
Q1. Explain why changes in air density will limit the resolution of ground-based telescopes.[3]
Q2. To what distance, in parsecs, can Gaia measure stars using the parallax method?[1]
Q3. Why is it important that other methods of distance measurement overlap with the range of star distances measurable by Gaia? [2]
Spectroscopic measurement of stellar distances
Q1. The diagram below shows the energy levels of the element hydrogen. Explain why only certain energy levels with integer quantum numbers exist. [3]
Q2. Astronomers use absorption spectra when assigning a star to a spectral class, which gives its luminosity. Part of the absorption and emission spectra of hydrogen are shown below.
(a)Passing an electric discharge through a gas will generate an emission spectrum like the one shown above. Explain how an emission spectrum arises in this case. [3]
(b)An absorption spectrum is obtained when dispersing light from the Sun through a prism or diffraction grating. Explain how an absorption spectrum arises. [3]
(c)The spectra shown above constitute the Balmer series, in which absorption or emission terminates on the n=2 energy level. Calculate the wavelengths of the first three Balmer absorption lines and verify that they appear in the correct location in the spectrum above.
(1 eV = 1.6 x 10-19 J, h = 6.6 x 10-34 Js)[6]
Q2. The intensity of absorption in the Balmer series can be used to determine the temperature of the star, leading to a determination of its luminosity. The Balmer absorption lines are weak at low temperatures because few electrons have been excited into the n=2 level from the n=1 (ground) level. Calculate the Boltzmann factor for excitation of an electron from the n=1 to the n=2 level at 5000 K and comment on the result. [3]
Q3. The Balmer absorption lines are also weak at very high temperatures. Explain why.[2]
Q4. Explain why apparent brightness shows an inverse-square variation with distance.[2]
Q5. Perform a test on the following data, which represent the intensity of radiation from the Sun at each of the inner planets, to show that solar radiation flux is falling off according to an inverse square relationship. [4]
PlanetMean distance from Sun (km)Solar flux at planet (W m-2)
Mercury 58 x 1069120
Venus108 x 1062640
Earth150 x 1061360
Mars228 x 106610
Q6. Show that K = 100 pc2 in the equation linking apparent brightness to absolute brightness and distance. [1]
Q7. Use the equation
apparent brightness = K x
to determine the distance to a star whose apparent brightness is 1.5 % of its absolute brightness.[2]
Q8. The star Deneb has an apparent brightness of 26 and absolute brightness of 65000 (arbitrary units). Calculate the distance to Deneb in parsecs. [2]
Q9. Would it be possible to measure the distance to Deneb using parallax? Explain your answer.[2]
Q10. The star Altair has an apparent brightness that is 4.2 times greater than its absolute brightness. Calculate the distance to Altair. [2]
Q11. Calculate the parallax angle for Altair. Would it be possible to measure its parallax angle with a ground-based telescope? [2]