TMA Quiz and Questions for Units 14-17

Question 1 – 10 marks
This question is designed to assess your engagement with interactive Quiz 5, covering Units 14, 15, 16 and 17.

(a) To demonstrate your engagement with Quiz 5, paste into your TMA answers a screenshot from your computer showing the marks you
obtained on the Quiz. It does not matter what score you obtained, we are only interested in whether or not you tried the Quiz. Remember
also that you may attempt the Quiz questions as often as you wish, and each question has multiple variants that will be presented to you in
turn, each time you try it. [2]

(b) In a few sentences, describe one thing that you learned from answering the questions in the Quiz that improved your understanding of either the behaviour of light or the behaviour of gases. You should not need to write more than 100 words to answer this part.  [4]

(Even if you scored full marks on the Quiz the first time you tried it,hopefully you learnt something of relevance in completing it. If you feel
that this was not the case, your statement to this effect should be supported by your screenshot in part (a).)

(c) (i) Identify one skill you need to develop that was identified in the general feedback you received on TMA 04 and explain what you
have done to develop this.

(ii) Identify a different skill you need to develop that was identified in comments on your submitted answers to TMA 04 and explain what
you have done to develop this.  [4]

You should not need to write more than 100 words to answer this part. (If your tutor did not identify any skills that you need to develop, you
should base your answers on a skill, or skills, that you have identified for development yourself.)

Question 2 – 15 marks
This question is designed to test your understanding of waves and wave propagation (Unit 14).

(a) In your own words:

(i) Use the Huygens principle to explain how plane parallel wavefronts are diffracted at a single aperture.

(ii) Use the principle of superposition to explain how coherent light emerging from two narrow slits can interfere to produce a pattern on a distant screen.   [9]

(b) A laser produces a beam of monochromatic light of wavelength 633 nm, which is incident normally on a diffraction grating whose slits are
vertical.

(i) Describe both the form and the colour of the diffraction pattern that is seen on a distant screen.

(ii) If the fifth order in the pattern is seen to occur at an angle of 39.3 with respect to the incident beam, how many lines per mm does the grating contain? [6]

Question 3 – 15 marks
This question is designed to test your understanding of lenses and optical systems (Unit 15). A converging lens of focal length f1 = +22.5 cm is placed at a distance d = 60.0 cm to the left of a diverging lens of focal length f2 = −30.0 cm. An object is placed on the common optical axis of the two lenses with its base 45.0 cm to the left of the converging lens. (The thin-lens approximation may be assumed to hold.)

(a) Calculate the location of the final image and its overall magnification with respect to the object. [6]

(b) Draw a ray diagram, to scale, illustrating the positions of the object, intermediate image and final image. Draw at least two key rays through
each lens to locate the positions of each image.   [7]

(c) Is the final image real or virtual? Is it erect or inverted?   [2]

Question 4 – 15 marks
This question is designed to test your understanding of the phases of matter (Unit 16). In your own words throughout, briefly explain:

(a) What is meant by the radial density function for molecules in a substance, and how it differs between a solid, a liquid and a gas [5]

(b) How the molecules move in a solid, a liquid and a gas, and how cooling allows one phase to be converted into another [5]

(c) How the van der Waals equation differs from the ideal gas equation of state, and what the additional terms in the former equation represent. [5]

Your explanations for each part should be less than about 150 words and may include an appropriate diagram. Marks will be deducted for answers that are too long.

Question 5 – 20 marks
This is designed to test your understanding of statistical mechanics (Unit 17).

(a) (i) In your own words, state Boltzmann’s two principles of statistical mechanics.   [2]

(ii) In the context of statistical mechanics, explain what is meant by a phase cell, and explain how such cells may be used in the specification of the configuration of a classical gas. [2]

(iii) In your own words, state Boltzmann’s distribution law for a gas in equilibrium.   [2]

(iv) Two phase cells in a gas in equilibrium are labelled X and Y. The probability of finding a given molecule in cell X relative to the probability of finding the molecule in cell Y is 125 and the temperature of the gas is 300 K. If the energy of cell X is 1.00 x 10−20 J, what is the energy of cell Y?   [4]

(b) A sealed container of volume V = 0.10 m3 holds a sample of N = 3.0 × 1024 atoms of helium gas in equilibrium. The distribution of speeds of the helium atoms shows a peak at 1.1 × 103 m s−1.

(i) Calculate the temperature and pressure of the helium gas. [7]

(ii) What is the average kinetic energy of the helium atoms? [3]

(Take the mass of each helium atom to be 4.0 amu.)