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KEELE UNIVERSITY
EXAMINATIONS, 2010/
Level I
Friday 14th^ January 2011, 16:00 - 18:
PHYSICS/ASTROPHYSICS
PHY-
Nature of Matter
Candidates should attempt ALL of PARTS A and B, and TWO questions from PART C. PARTS A and B should be answered on the exam paper; PART C should be answered in the exami- nation booklet which should be attached to the exam paper at the end of the exam with a treasury tag. PART A yields 16% of the marks, PART B yields 24%, PART C yields 60%.
Please do not write in the box below A C1 Total B C C C
NOT TO BE REMOVED FROM THE EXAMINATION HALL
PART A Tick the one box by the answer you judge to be correct (marks are not deducted for incorrect answers)
A1 The molecules in 1 kg-mole of an ideal diatomic gas rotate but do not vibrate. The internal energy of the gas, according to the classical Equipartition Theorem, is 1 2 RT^
3 2 RT^
5 2 RT^
7 2 RT^ [1]
A2 An isolated system is taken very slowly from an initial state to a final state. During this process, an amount of heat Q enters the system, and work W is done by the system. What other property of the system changes during this process? chemical composition mass temperature number of moles [1]
A3 If a system undergoes an isothermal change then
its temperature rises at a constant rate there is no exchange of energy with the surroundings no work is done on or by the system the temperature of the system stays constant [1]
A4 The Kinetic Theory of gases works best for
diatomic gases gases just above their liquefaction point gases at low densities gases at very high densities [1]
A5 On a phase diagram, the triple point describes the point at which
three different gases can co-exist independently in a gas mixture all three phases of a substance (gas, liquid, solid) can co-exist the point at which tri-atomic gases (such as CO 2 ) are found a solid can exist in three different crystalline forms [1]
A12 Which of the following indicate the photon (i.e. ‘particle’) nature of electromagnetic radiation? interference the Compton effect constancy of speed in any inertial reference frame diffraction [1]
A13 Classical physics fails to explain the photoelectric effect because the measured kinetic energy of the emitted electrons depends on the intensity of the incident light depends on the frequency of the incident light does not depend on the properties of the incident light is the same for all surfaces [1]
A14 18 O and 16 O are both isotopes of oxygen because they
contain the same number of neutrons in the nucleus contain the same number of particles in the nucleus contain the same number of protons in the nucleus contain the same number of electrons in the nucleus [1]
A15 The binding energy of an atomic nucleus is
the energy needed to disperse its constituent nucleons the total energy of its constituent nucleons (including rest mass) the total energy of the electrons in the nucleus (including rest mass) the sum of the kinetic energies of its constituent nucleons [1]
A16 In the nuclear reaction 126 C + 126 C → 2010 Ne + X, identify X: (^63) Li 146 C 42 He 31 H [1]
/Cont’d
PART B Answer all EIGHT questions
B1 A gas at pressure P is contained in a cylindrical vessel. The gas does work on a friction-free piston by raising it by a small distance dx. Show that the work done by the gas is dW = P dV , where dV is the change in gas volume. [3]
B2 For an ideal gas at temperature T , each degree of freedom can be ascribed a mean energy 12 kBT. Use this to determine the internal energy U for 1 kg of an ideal monatomic gas having atomic weight A. [3]
B5 What is the de Broglie wavelength associated with a neutron which has kinetic energy 10 keV? [3]
B6 A radio transmitter operating at frequency 3 000 MHz has power 2 W. How many photons does it emit per second? [3]
B7 In a photoelectric effect experiment, a metal with work function 3.1 eV is irradiated with radiation. If the maximum kinetic energy of the ejected electrons is 1.87 eV what is the wavelength of the incident radiation? [3]
B8 Sketch the dependence of the binding energy per nucleon for atomic nuclei as a function of atomic mass. [3]
/Cont’d
C3 (a) Describe the photoelectric effect, and explain why it can not be understood on the basis of classical physics. [10] (b) Outline Einstein’s theory of the photoelectric effect. [10] (c) In a photoelectric effect experiment, monochromatic radiation of wavelength λ = 260 nm is incident on a metal surface. The maximum kinetic energy of the ejected electrons is found to be 1.55 eV. What is the work function for the metal, and what is the maximum electron kinetic energy if radiation with λ = 395 nm is used? [10]
C4 (a) Radiation is used to observe an electron. Show that the uncer- tainty in the position of the electron, ∆x, and the uncertainty in its momentum, ∆p, are related by
∆x ∆p ≃ h ,
where h is Planck’s constant. [10] (b) What is an alternative form of the Uncertainty Principle? [2] (c) An alpha particle (^42 He) is confined within an atomic nucleus, of dimensions ∼ 7 × 10 −^15 m. Assuming its speed is ≪ c, what is the uncertainty in its speed? [8] (d) A photon of wavelength 500 nm forms a virtual e−^ e+^ pair. Es- timate the time that elapses before the photon is reconstituted. [10]
