1. (i) \(CH_3—CH_2—CH(Br)—CH_3\)

(ii) \(\% \text{ yield} = \frac{\text{actual yield}}{\text{theoretical yield}} \times 100\)

From equation of reaction, \(136.9 \text{ g of } C_4H_9Br \rightarrow 74 \text{ g of } C_4H_9OH\)

\(\Rightarrow 8.72 \text{ g is expected to produce } \frac{8.72 \times 74}{136.9} = 4.71 \text{ g of } C_4H_9OH\)

\(\Rightarrow \text{Theoretical yield of } C_4H_9OH = 4.71 \text{ g}\)

Actual yield = \(4.28 \text{ g}\)

\(\Rightarrow \% \text{ yield} = \frac{4.28}{4.71} \times 100 = 90.87 \% \)

2. change in momentum, \(\Delta P = mv – mu\)

\(v = 32 \text{ m s}^{-1}\) and \(u = 0 \text{ m s}^{-1}\)

\(\Rightarrow \Delta P = 0.44(32) – 0.44(0) = 14.08 \text{ kg m s}^{-1}\)

3. (i) \(P = IV\)

\(I = \frac{P}{V} = \frac{30}{120} = 0.25 \text{ A}\)

(ii) \(Q = It\)

\(I = 0.25 \text{ A}, \quad t = 3\text{hrs} = 3 \times 60 \times 60 = 10800 \text{ s}\)

\(Q = 0.25 \times 10800 = 2700 \text{ C}\)

The charge of \(1 \text{ e}^- = 1.60 \times 10^{-19} \text{ C}\)

\(\Rightarrow \text{number of electrons} = \frac{2700}{1.60 \times 10^{-19}} = 1.69 \times 10^{22}\)

4. (i) The cylinder is in equilibrium when the upward forces balance its weight.

i.e. Upthrust (U) + tension in wire (T) = weight of cylinder (W)

(ii) \(U = W – T = 5.3 – 4.8 = 0.5 \text{ N}\)

\(U = \rho V g\)

Volume of cylinder, \(V = Ah\)

\(\Rightarrow U = \rho A h g\)

\(A = 13 \text{ cm}^2 = 13 \times 10^{-4} \text{ m}^2\)

\(h = 5 \text{ cm} = 5 \times 10^{-2} \text{ m}\)

\(\rho = \frac{U}{Ahg} = \frac{0.5}{13 \times 10^{-4} \times 5 \times 10^{-2} \times 9.81} = 784.13 \text{ kg m}^{-3}\)

5. (i) number of protons = 95
number of neutrons = 146

(ii) some of the energy was gained by the Neptunium nucleus.

6 (i) ionic bond

(ii) The ions in solid sodium chloride are not free to move. In aqueous solution the ionic bonds are broken and ions are free to move.

• Good electrical insulators
• Resistant to corrosion (chemically inert)
• Tough / durable
• Low thermal conductivity

(ii) Thermoplastics soften when heated and can be easily remoulded so they can be recycled. Thermosetting plastics cannot be remoulded and are more brittle.

(iii) \(\text{tensile strength, } \sigma = \frac{F}{A} = \frac{900}{25 \times 10^{-6}} = 3.6 \times 10^7 \text{ Pa} = 36 \text{ MPa}\)

Comment: The plastic is suitable for making chairs because its tensile strength of 36 MPa lies within the range of 25 – 40 MPa.

(b) (i) principal axis of a lens is the straight line that passes through the optical centre of a lens and is perpendicular to lens surfaces.

Real image: is an image formed when light rays actually converge, and can be projected onto a screen.

(ii) [Ray Diagram Placeholder]

\(\frac{1}{f} = \frac{1}{u} + \frac{1}{v}\)

\(f = 15 \text{ cm}, \quad u = -30 \text{ cm}\) (Object distance is negative per sign convention)

\(\Rightarrow \frac{1}{15} = \frac{1}{-30} + \frac{1}{v} \Rightarrow v = 10 \text{ cm}\)

(iii) – Optical fibers transmit data faster over longer distances with less signal loss.
– They are not affected by electromagnetic interference, resulting in clearer communication.

(c) (i) Saturated Hydrocarbon: a compound of carbon and hydrogen only which contain only single bonds between the carbon atoms.

Fractional Distillation: the separation of a mixture of liquids based on the difference in boiling points.

Cracking: the breaking down of large hydrocarbon chains to smaller ones by heat.

(ii) let the compound formed = \(C_xH_y\)

\(\Rightarrow C_{16}H_{34} \rightarrow 2C_2H_4 + C_3H_6 + C_xH_y\)

Number of atoms of each element on both sides of the equation are same.

\(\Rightarrow \text{carbon atoms: } 16 = 2(2) + 3 + x \Rightarrow x = 9\)

\(\Rightarrow \text{hydrogen atoms: } 34 = 2(4) + 6 + y \Rightarrow y = 20\)

So, the equation of the reaction is: \(C_{16}H_{34} \rightarrow 2C_2H_4 + C_3H_6 + C_9H_{20}\)

(iii) Limited oxygen, poor fuel-air mixing, low combustion temperature.