NJC 2022 Prelim P3

[Turn over NATIONAL JUNIOR COLLEGE SENIOR HIGH 2 PRELIMINARY EXAMINATION Higher 2 CANDIDATE NAME SUBJECT CLASS REGISTRATION NUMBER PHYSICS Paper 3 Structured Questions Candidate answers on the Question Paper. 9749/03 26 Aug 2022 2 hours No Additional Materials are required. READ THE INSTRUCTION FIRST Write your subject class, registration number and name in the spaces at the top of this page. Write in dark blue or black pen on both sides of the paper. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Section A Answers all questions. Section B Answer one question only. You are advised to spend one and a half hours on Section A and half an hour on Section B The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 / 10 2 / 12 3 / 14 4 / 10 5 / 6 6 / 8 Section B 7 / 20 8 / 20 Total (80) This document contains 24 printed pages and 4 blank pages.

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4 Section A Answer all the questions in the spaces provided. 1 If an object is projected vertically upwards from the surface of a planet at a fast enough speed, it can escape the planet’s gravitational field. This means that the object can arrive at infinity where it has zero kinetic energy. The speed that is just enough for this to happen is known as the escape speed. (a) r is the distance from the centre of the planet. On Fig 1.1, draw the variation with distance r of the kinetic energy EK, gravitational potential energy EP and the total energy ET of this object from the surface of the planet. Fig. 1.1 [3] (b) (i) By equating the kinetic energy of the object at the planet’s surface to its total gain of potential energy in going to infinity, show that the escape speed v is given by v2= 2GM R where R is the radius of the planet and M is its mass. [1] energy r surface of planet 0

[Turn over 5 (ii) Hence show that v2 = 2Rg where g is the acceleration of free fall at the planet’s surface. [2] (c) The mean kinetic energy Ek of an atom of an ideal gas is given by Ek = 3 2 kT where k is the Boltzmann constant and T is the thermodynamic temperature. (i) Using the equation in (b)(ii), estimate the temperature at the Earth’s surface such that helium atoms of mass 6.6 × 10–27 kg could escape to infinity. You may assume that helium gas behaves as an ideal gas and that the radius of Earth is 6.4 × 106 m. temperature = ..................................................................... K [3] (ii) The temperature estimated in (i) is measured in thermodynamic scale. Explain what is absolute zero in the thermodynamic scale. …………………………..…….…………...………………………………………………………… …………....…………………………………………………………………………….…............. [1] [Total: 10]

6 2 A container contains an ideal gas at a thermodynamic temperature T. The kinetic theory of gas assumes that the molecules of the gas behave as hard, identical spheres that are in continuous random motion. The theory shows that • the pressure exerted on the wall of the container by the gas is due to the elastic collisions of the molecules with the wall of the container • the pressure is proportional to the mean-square speed of the molecules • the mean translational kinetic energy of a molecul e is EK = 3 2 kT where k is the Boltzmann constant. (a) Explain why the internal energy of the gas is equal to the total kinetic energy of the molecules of the gas. .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .………………………………………………………………………………………………………….. [3] (b) A container with 1.2 mol of an ideal gas. The gas has a mass of 0.0384 kg. During the heating of the gas, • the volume of the gas increases (the container does not have a fixed volume) • the pressure of the gas remains constant • the temperature of the gas changes from 280K to 460K • the gas does 1.3 × 103 J of work. (i) Explain, in terms of the force produced by the molecules of the gas, how the pressure remains constant as the volume increases. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .…………………………………………………………………………………………………… [3]

[Turn over 7 (ii) Use the first law of thermodynamics to determine the specific heat capacity of the gas. specific heat capacity = ……………………………………….. J kg–1 K–1 [4] (c) The container in (b) is now replaced with one that has a fixed volume. Thermal energy is supplied to the gas to increase its temperature from 280K to 460K. Suggest, with a reason, how the specific heat capacity of the gas would now compare with the value in (b)(ii). .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .………………………………………………………………………………………………………….. [2] [Total: 12]

8 3 Hydrogen gas at low pressure can be made to emit photons in a discharge tube using a high voltage supply, as shown Fig. 3.1. Fig. 3.1 The photons are incident normally on a diffraction grating and projected on a screen. An emission line spectrum is observed. (a) Explain what is meant by emission line spectrum. .……………………………………………………………………………………………………………… .………………………………………………………………………………………………………….. [1] (b) Explain how the line spectrum of the hydrogen provides evidence for the exi stence of discrete energy levels in atoms. .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .………………………………………………………………………………………………………….. [3] discharge tube with low pressure hydrogen gas high voltage source + – diffraction grating

[Turn over 9 (c) Some electron energy levels in atomic hydrogen are illustrated in Fig. 3.2. Fig. 3.2 (not to scale) The electron transitions A and B cause light of visible wavelengths 654 nm and 488 nm to be emitted. Explain why the third transition C in Fig. 3.2 cannot be observed. .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .……………………………………………………………………………………………………………… .………………………………………………………………………………………………………….. [3] A B C –0.85 eV –1.50 eV –3.41 eV energy

10 (d) The central maximum and the first order maxima of the two visible wavelengths from the hydrogen gas in (c) on the screen is shown in Fig. 3.3. Fig. 3.3 (not to scale) The screen is placed 240.0 cm from the diffraction grating. The maxima positions on a scale on the screen is shown. (i) Explain how the diffraction and the interference of light at the diffraction grating leads to the first order maxima for λ1. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .………………………………………………………………………………………………………. .…………………………………………………………………………………………………… [3] (ii) Determine th