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(a) The statement means that an electric charge of 5\(\mu\)F is stored by the fully charged capacitor when connected to a d.c source of 1V. (b)(i) (i) Factors (ii) Form of dependence - Common area of plates - Distance between plates - Permitivity or nature of dielectric - Direct proportionality - Inverse proportionality - Direct proportionality (c)(i) (ii) \(\frac{1}{C} = \frac{1}{C_1} + \frac{1}{C_1} + \frac{1}{C_3}\) = \(\frac{1}{8} + \frac{1}{12} + \frac{1}{20} = \frac{3 + 2 + 1}{24}\) C = \(\frac{24}{6} = 4 \mu F\) (iii) Q = CV = 4 x 10\(^{-6}\) x 90 = 360\(\mu\)C charge on 8\(\mu\) FV = \(\frac{Q}{C} = \frac{360}{8}\) = 45V

(a) \(^{14}_7 + ^1_0n\) -> \(^4_2He + ^{11}_5X\) (b)(i) The radioactive atom disintegrates spontaneously while a stable atom does not disintegrate on its own. (ii) The time at which the number of radioactive atoms remaining is just one-half of the original number is called half-life of the element. The half-life T\(_{\frac{1}{2}}\) is related to the decay constant (\(\lambda\)) of the isotope by the equation. \(T \frac{1}{2} = \frac{0.693}{ \lambda}\) (iii) After 35days, 1/2 of it remains. After 70 days, 1/2 of 1/2 i.e. 1/4 remains. After 105 days, % of 1/4 i.e. 1/8 remains. (c)(i) The photon energy Ep = hf = \(\frac{hc}{f}\) = \(\frac{6.6 \times 10^{-34} x 3.0 \times 10^8}{ 5.0 x 10^{-7}}\) = 3.96x 10-19J (ii) The kinetic energy E\(_k\) = (Ep - W) E\(_k\) = hf - W = \(\frac{hc - W}{\lambda}\) W = 1.9eV = 1.6 x 10\(^{19}\) x 1.9 = 3.044 x 10\(^{-19}\)J. E\(_k\) = 3.96 x 10\(^{-19}\) - 3.044 x 10\(^{19}\) = 9.2 x 10\(^{-20}\)J. (iii) Stopping potential Vs = energy needed to stop most energetic electron. eVs =E\(_{kmax}\) Vs = \(\frac{E_{max}}{e}\) = \(\frac{9.20 \times 10^{-20}}{1.6 \times 10^{-19}}\) = 0.575 V

Table of values Vcm Ucm 10.0 47.0 15.0 48.3 20.0 49.4 25.0 51.20 30.0 52.50 35.0 54.00 Slope = \(\frac{Du}{DN} = \frac{13}{47}\) = 0.28 The intercept (c) on the vertical axis = 44cm (i) \(K_1\) = \(\frac{(1-2s)}{s}\)100 = \(\frac{1-0.56}{0.28}\)100 = 157 (ii) \(K_2\) = \(\frac{2c}{s}\) - 160 = \(\frac{2 \times 44}{0.28}\) - 160 = 154.3 Precautions: I Avoid draught. I Ensure mass does not rest on the table I avoid errors due to parallax when reading metre rule. (b)i. The conditions under which a rigid body remains in equilibrium when acted upon by three non-parallel coplanar forces are: The forces must be concurrent (i.e. they must meet at a point. The resultant of the forces must be equal to zero. The forces can be represented in magnitude and direction by the sides of a triangle taken in order. A body is in stable equilibrium if the vertical line through the centre of gravity falls outside the base of support when the body is slightly titled

Table of values Icm\(^{3}\) hcm\(^{3}\) 10.0 7.50 15.0 11.25 20.0 15.00 25.0 18.75 30.0 22.50 Slope (s) = \(\frac{\bigtriangleup {h}}{\bigtriangleup {|}} = \frac{12.50}{20.00}\) = 0.625 Evaluate: (i) \(K_1\) = 1 - S = 1 - 0.625 = 0.375 (ii) \(K_2\) = \(\frac{1}{K} = \frac{1}{0.375}\) = 0.67 Precautions: The lower level of the meniscus of water is read at eye level. Parallax error is avoided in reading the scale to determine h and I Zero error of metre rule is noted. (b)0) Total internal reflection of light occurs when light travels from a dense medium to a less dense medium so that the angle of incidence (in the dense medium) is greater than the critical angle ii. Let apparent upward displacement of points be t, real depth, D = 6cm. Therefore apparent depth = D - t = 6 - t Refractive index aug =1.5 = \(\frac{\text {Real depth}}{\text {Apparent depth}}\) = 1.5 = \(\frac{6}{6 - t}\), (6-t) x 1.5 = 6cm \(\therefore\) 9-1.5t = 6 i.e t = \(\frac{9-6}{1.5}\) = 2.0cm OR Refractive index a\(\mu\)g = \(\frac{\text {real depth}}{\text {apparent depth}}\) \(\therefore\) Apparent depth = \(\frac{\text {real depth}}{a \mu g}\) = 6 = 4 1.5 Displacement = real depth - apparent depth = (6 - 4) cm = 2.0cm

Table of values L(cm)\(^{3}\) Ls(cm) Lp(cm) \(R_1\) 100 5.3 94.7 17.90 90 6.5 93.5 14.40 80 7.0 93.0 13.30 70 8.5 91.5 10.80 60 9.5 90.5 9.50 L(cm) Is\(^{1}\) Lg \(R_2\) 100 21.60 78.4 3.60 90 22.1 77.9 3.50 80 23.4 76.6 3.30 70 24.3 75.7 3.10 60 25.3 74.7 2.95 L(cm) Ls(cm) Lp(cm) \(R_1\) Ls\(^{1}\)cm\(^{3}\) Lq R\(^{2}\) 100 5.3 94.7 17.90 21.6 78.4 3.60 90 6.5 93.5 14.40 22.1 77.9 3.50 80 7.0 93.0 13.30 23.4 76.6 3.30 70 8.5 91.5 10.80 24.3 75.7 3.10 60 9.5 90.5 9.50 25.3 74.7 2.95 Slope (s) = of the graph = \(\frac{DR_{2}}{DR_{1}} = \frac{1.4}{8.0}\) = 0.175 K = \(\sqrt 5\) = 0.17555 = 0.42 Precautions: Key was opened where readings were not being taken. Tight connections were ensured ParallaX errors were avoided in reading the metre rule. Zero error was noted in reading the metre rule. The jockey was not rolled on or allowed to scratch the wire. (b) The resistivity of a material is defined as the resistance of a unit length of the material/wire of a uni cross-sectional area. OR P = \(\frac{AR}{L}\) where A = cross-sectional area R = eletrical resistance L = length of the wire V = Vg + \(V_R\) = IRg + IR = I (Rg + R) \(\therefore\) \(\frac{V}{I}\) = Rg+ R = \(\frac{1.5}{1.5 \times 10^{-3}}\) = 50 + R = 10\(^{3}\) = 50 + R \(\therefore\) R = 950\(\Omega\)

According to Avogadro's law which states that equal volumes of different gases contain the same number of molecules at the same temperature and pressure. If the number of molecules gas X contains, is Z molecules, therefore, gas Y will also contain Z molecules. Option C is the correct answer

\(2H_2 + O_2 → 2H_2O\) 4g → 36g 8g → X X → \(\frac{ 36 \times8}{4}\) = 72.0g

If it were a neutral atom,the number of proton would have been equal to number of electron = 9 each However, since the number of electrons is by 1 greater than that of proton, and since electrons having more number than proton are negatively charged, the particle must be a negative ion.

Gamma rays are used to treat cancer as part of a type of cancer treatment called radiation therapy. Gamma rays can pass through several inches of lead or a few feet of concrete. They can even pass through the human body, damaging tissue and DNA.

In 1910, Millikan successfully measured the charge of the electron to be 1.6 x 10\(^{-19}\)C. Positive rays were discovered by Eugen Goldstein, in 1886. J.J. Thomson discovered the charge-to-mass ratio of an electron in 1897: Cathode rays were discovered by. J. J. Thomson

Element Z has electronic configuration of 2, 8, 8, 2. This implies it's in group 2 (Alkaline earth metals). Actually, the element is most likely to be Calcium with an atomic number of 20. The correct answer is option C

168X, m8X [\(\frac{90}{100}\times 16\)] + [\(\frac{10}{100}\times m\)] = 16.2 14.4 + 0.1m = 16.2 0.1m = 1.8 m = \(\frac{1.8}{0.1}\) m = 18

The average kinetic energy of a gas's molecules increases as the temperature of the gas increases.The kinetic energy of a gas is directly proportional to its temperature. This means that as the temperature of a gas increases, so does the average kinetic energy of its molecules.

The movement of ships helps break up the oil slick, increasing its surface area and promoting natural dispersion by wave action and microbial degradation. The other options are incorrect. The is the reason: A. Pouring detergents – While detergents can break oil into smaller droplets, they can also introduce harmful chemicals into the water, affecting aquatic life. C. Pouring organic solvents – This is harmful as it can introduce toxic chemicals into the water, worsening pollution. D. Evaporation – While some lighter fractions of oil can evaporate, this is a slow process and does not effectively disperse the pollution.

Deliquescent substances are used for drying because they can absorb and hold a large amount of moisture. Hence, they are often used as drying agents.