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(a) A discharge tube at very high p.d. filled with neon and evacuated to a very low pressure of about 5mm will produce a discharge between the electrodes with a characteristic colour. (b) The colour depends on; - nature of the gas in the tube. -nature of coating inside the tube

When a D.C is a applied, the positive ions of the electrolyte are attracted to the cathode and the appropriate ions are discharged and deposited. But if an A.C. is used, the mass deposited during one half of the cycle will be completely removed during the next half cycle, hence there will be no electroplating.

(a)(i) A machine is a device by means of which a force or effort applied at one point is used to overcome load at the other point. (ii) Examples of simple machines are: lever, pulley system, incline plane, Jack, wheel and axle and hydraulic press (iii) This means that the distance moved by the effort is 5 times the distance moved by the load at the same time interval. (b)(i) Efficiency of a machine is the ratio of work output to work input expressed in percentage. (iii) The efficiency of a machine can never be 100% because part of the energy supplied to the machine is used to overcome friction and in moving other parts of the machine. (i) Velocity ratio, V.R = \(\frac{2 \pi r}{P} = \frac{2 \pi \times 40}{0.4}\) = 628 (ii) Efficiency = \(\frac{M.A}{V.R}\) x 100% M.A. = \(\frac{\text{Efficiency x V.R}}{100}\) = \(\frac{25 \times 628}{100}\) = 157 (ii) M.A = \(\frac{load}{Effort}\); Effort = \(\frac{load}{M.A}\) = \(\frac{1000}{157}\) = 6.4N

(a)(i) Relative density is the ratio of the density of the substance to the density of water (ii) Characteristics of pressure in liquid are: -pressure increases in direct proportion to the depth of the liquid -pressure at any point in a liquid acts equally in all directions -pressure at all points at the same level within a liquid is the same -pressure applied to an enclosed liquid is transmitted equally throughout the fluid. (b) Force on the door F = Ah g = 0.4 x 500 x 1.03 x 103x 10 = 2.06x 106N (c)(i) Effects of heat other than expansion are: -Rise in temperature -Change of state -Change of colour -Change of electrical resistance (ii) When a liquid and its vapour are in dynamic equilibrium, the vapour is said to be saturated. The pressure or force exerted on unit area of the container of such a saturated vapour is known as saturated vapour pressure. (iii) Heat generated by coil = heat gained by water + container. \(\frac{V^2t}{R}\) = mc\(\theta_{\text{water}}\) + Q\(_c \theta_{\text{container}}\) \(\frac{220^2 \times 2 \times 2 \times 60}{20}\) = m x 4.2 x 10\(^{3}\) x 60 + 100 x 60 290400 = 252000m + 6000 m = \(\frac{290400 - 6000}{252000}\) = 1.13kg

(a) Heisenberg's uncertainty principle states that there is always an uncertainty in any attempt to measure the position and momentum of a particle simultaneously (b) Phenomena explained in terms of particle nature of light are: - photoelectricity, - black body radiation, - compton effect

(a)(i) Principal focus of a convex mirror is a pc.nt on the principal axis on which all rays parallel and close to the principal axis appear to diverge after reflection. (ii) The pole is the centre of the mirror through which the principal axis pass. (iii) Radius of curvature is the radius of the sphere from which the mirror was cut. (b) Advantages of using convex mirror for driving -wide field of view -image is always upright. Disadvantages of using convex for driving: -image is smaller -image appears further away and gives false impression of the distance. (d)(i) \(\frac{1}{u} + \frac{1}{v} = \frac{1}{f}; \frac{1}{u} - \frac{1}{30} = \frac{1}{10}; \frac{1}{u} = \frac{1}{10} + \frac{1}{30}\) = \(\frac{4}{30} = \frac{2}{15}; u = \frac{15}{2}\) = 7.5cm (ii) \(\frac{\text{image size}}{\text{object size}} = \frac{\text{image distance x object size}}{\text{object distance}}\) = \(\frac{30 \times 0.25}{7.5} = 1cm\) (iii) Power = \(\frac{1}{\text{focal length (in metre)}} = \frac{1}{0.1}\) = +10.0 dioptre 0.1

(a)(i) Reactance s the opposition in ohms to the alternating current by an inductor, a capacitor or both. (ii) Impedance is the total opposition is ohms to the alternating current by a combination of resistor as well as a capacitor or an inductor. (b)(i) Resonant frequency fo is to frequency at which the current in the circuit has a maximum value. fo = \(\frac{1}{2 \pi LC}\) (ii) This means that the root mean square value of the voltage is 230v. The actual voltage lies between Vo and -Vo where the voltage amplitude or peak voltage Vo. (c)(i) \(V^2 = V^2_R + (V_L - V_C)^2; 240^2 = 140^2 + (50 - v_c)^2\); 50 - \(V_c = 194.9\) \(V_c = 244.9v\) (ii) X\(_c = \frac{1}{2 \pi fc} = \frac{V}{1} = \frac{1}{2 \pi \times 50 \times c} = \frac{244.9}{10}\) C = \(\frac{10}{2 \pi \times 50 \times 244.9} = 129.97 \mu F\) (iii) \(X_L = 2 \pi fL = \frac{v}{l}; 2 \pi \times 50 \times L = \frac{50}{10}\) L = \(\frac{50}{100x}\) = 0.01159Hz (d)

a)(i) Nuclear fission is a nuclear reaction in which a heavy nucleus is split into different lighter nuclei emitting neutrons with the release of a large amount of energy. (ii) Nuclear fusion is a nuclear reaction between two light nuclei at high temperatures formic a heavier nucleus with the release of a large amount of energy. (b)(i) Applications of atomic energy are: - for the production of nuclear weapons for warfare - in the generation of electric power - for health diagnosis and radiotherapy - to detect leakages. In underground pipes carrying oils or gases. (ii) Half life is the time required for radioactive substance to decay to half of its original quantity. (iii) T = \(\frac{0.693}{\lambda}\) (c)(i) \(^{226}_{88} X \) ---> \(^{222}_{88} Y + ^4_2He\) By the emission of \(\alpha\) the mass number of X decreases by 4 the atomic number by 2 to give daughter nucleus Y (ii) \(^{222}_{86} Y \) ---> \(^{222}_{87} Z + ^0_{-1} e\) By the emission of \(\beta\) particle the mass number of Y is unchanged while the atomic number of Y is unchanged while the atomic number is increased by 1. (iii) \(^{226}_{87} Z \) ---> \(^{222}_{87} Z + ^0_0\gamma\) By emission of \(\gamma\) radiation, the mass and atomic number of Z remain unchanged.

Table of values i^\circ \(\theta\) Cos\(\theta\) Sin i 5^\circ 81^\circ 0.156 0.087 10^\circ 74^\circ 0.276 0.174 15^\circ 69^\circ 0.358 0.259 20^\circ 61^\circ 0.484 0.342 25^\circ 51^\circ 0.629 0.423 Slope = \(\frac{x_{2}-x_{1}}{y_{2}-y_{1}}\) = \(\frac{0.6-0.1}{0.4-0.05} = \frac{0.5}{0.35}\) = 1.43 Precautions: Avoid error due to parallax The direction of the light rays must not be blocked when fixing the search pin or viewing through the glass prism The optical pins must be straight and not bend. (b)i. The first law of refraction of light states that the incident ray, the reflected ray, and the normal ray at the point of incidence all lie in the same plane. The second law of refraction of light states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is a constant for the media concerned. i.e, \(\frac{\text {Sin i}}{\text {Sin r}}\) = a constant (i1) The statement, "the refractive index of a material is 1.65" means that the ratio of the speed of light in a vacuum to the speed of light in the medium is numerically equal to 1.65. i.e; Refractive index (n) = \(\frac{\text {speed of light in vacuum}}{\text {speed of light in the medium}}\) = 1.65 The refractive index of any medium depends on the wavelength of the incident light.

Table of values XY = 100cm R(\(\Omega\)) 1(amp) V 0 0.15 2.65 1 0.15 2.65 5 0.15 2.65 10 0.10 1.85 20 0.08 1.40 40 0.06 0.90 60 0.04 0.70 Slope = \(\frac{x_{2}-x_{1}}{y_{2}-y_{1}} = \frac{1.75-0.5}{0.10-0.025} = \frac{1.25}{0.075}\) Precautions: I ensured good contact and the correct connection of the circuit. I avoided incorrect positioning of the eye (error due to parallax). Open the key plug when recording the reading taken. (b)i. The experiment is based on Ohm's law. Ohm's law states that the current flowing through a metallic conductor is proportional to the potential difference between its ends provided the temperature and other physical conditions of the conductor remain constant; i.e: \(\frac{V}{|}\) = Constant. ii. Area of cross-section of wire = \(\frac{\pi d^{2}}{4} = \frac{\frac{22}{7} \times (0.2)^{2}}{4}\) \(\frac{3.143 \times 0.04}{4}\) = 0.031mm\(^{2}\) = 3.1m\(^{2}\) Resistivity = \(\frac{RA}{L}\), length (L) = \(\frac{R.A}{resistivity}\) = \(\frac{7 \times 3.1}{8.8 \times 10^{-7}} = \frac{21.7}{8.8 \times 10^{-7}}\) = 2.47 x 10\(^{-7}\)

K- (31.91%), Mole = 31.91/39 =0.8182 Cl-(28.93%), Mole = 28.93/35.5 = 0.815 O-(39.16%), Mole = 39.6/16 = 2.448 K = 0.8182/0.815 = 1 Cl = 0.815/0.815 = 1 O = 2.448/0.815 = 3

The empirical formula is the simplest whole number ratio of the number of atoms of each element in a substance. In the case of ethanoic acid, the ratio of atoms is 1:2:1, as shown by the empirical formula CH\(_2\)O. The molecular formula for ethanoic acid is C\(_2\)H\(_4\)O\(_2\).

Trichloromethane (Chloroform) being in smaller quantity and ethanol being in large quantity means trichloromethane is the impurity while the ethanol is the pure substance. As we know, impurities in pure substances tend to increase their boiling point. Consequently, if the boiling point of ethanol (pure substance) is 78\(^0\)C, with the introduction of impurity (trichloromethane), the boiling point will increase from 78\(^0\)C. Among the options, the only temperature range that has a boiling point higher than 78\(^0\)C is option C (82 - 84\(^0\)C).

Chromatography is a laboratory technique for the separation of a mixture into its components. A mixture is dissolved in a mobile phase, which is a liquid or gas that flows through a stationary phase, which is a solid or liquid. The components of the mixture separate as they travel through the stationary phase because they have different affinities for it. The chromatography separation of ink is based on the ability of the components to move at different speeds in the column.

Le Chatelier's principle states that if a dynamic equilibrium is disturbed by changing the conditions, the position of equilibrium shifts to counteract the change to reestablish an equilibrium. For the backward reaction to be favoured(LHS) , the concentration of one of the reactants must be reduced. i.e either E or F must be reduced. However, from the option, option C happens to be the one that fits in, as E is the only reactant reduced.