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h = \( 6.6 \times 10^{-34}\)Js, 1eV = \( 1.6 \times 10^{-19}\)J, \(E_1\) = - 8.6eV, \(E_2\) = - 3.5eV, f = ? \DeltaE = hf f = \(\frac{\DeltaE}{h}\) \DeltaE = \(E_2\) - \(E_1\) = - 3.5eV - (- 8.6eV) = 5.1eV but 5.1eV = 5.1 X \( 1.6 \times 10^{-19}\) = \( 8.16 \times 10^{-19}\)J f = \(\frac{8.16 \times 10^{-19}}{ 6.6 \times 10^{-34}}\) Therefore, f = \( 1.24 \times 10^{15}\)Hz

The statement that explains the observation is: The most energetic molecules leave the surface and escape into the air. This phenomenon is known as evaporation. In a liquid, molecules have varying energies, and the molecules with higher kinetic energies (the most energetic ones) are more likely to overcome the attractive forces within the liquid and transition into the gaseous phase. These molecules escape from the surface of the liquid into the air, gradually reducing the amount of liquid in the open dish. Evaporation is a process that occurs continuously as long as there is a liquid exposed to the air.

The specific latent heat of vaporization of lead is the amount of thermal energy required to change 1 kg of molten lead to vapor at constant temperature and pressure.

\(v_P = 30 ms^{-1}\), \(v_Q = 20 ms^{-1}\) \(v_P = v_Q + v_{P/Q}\) \(v_{P/Q} = v_P - v_Q\) = 30 - 20 ∴ \(v_{P/Q} = 10 ms^{-1}\)

When a lightweight body and a massive body are acted upon by the same force for the same time, the momenta of both bodies remain the same. Given that the momenta of both the heavy and light bodies are the same, it follows that the light body possesses a higher velocity compared to the heavy body.

Distance between X and Y is the area of rectangular portion of the velocity-time graph. XY = 40 \times (8 - 4) = 40 \times 4 ∴ XY = 160 m

f = 512Hz, V = 331m/s \lambda = ? V = f \lambda \lambda = \(\frac{v}{f} = \frac{331}{512}\) \lambda = 0.646m.

The work done in moving a charge across a potential difference is given by the formula W = QV, where W is the work done, Q is the charge and V is the potential difference. Substituting the given values, we get W = 10 C * 220 V = 2200 J. Hence, the work done is 2200 J.

Maximum Range R = \(\frac{u^2sin2\theta}{g}\) maximum height H = \(\frac{u^2sin^2\theta}{2g}\) But R : H = 4 \(\frac{u^2sin2\theta}{g}\) : \(\frac{u^2sin^2\theta}{2g}\) = 4 \(\frac{u^2sin2\theta}{g} \times\frac{2g}{u^2sin^2\theta}\) = 4 \(\frac{2sin2\theta}{sin^2\theta}\) = 4 since 2sinΘ = 2sinΘcosΘ \(\frac{2 \times 2sin\theta cos\theta}{sin^2\theta}\) = 4 \(\frac{4sin\theta cos\theta}{sin^2\theta}\) = 4 \(\frac{sin\theta cos\theta}{sin^2\theta}\) = 1 \(\frac{cos\theta}{sin\theta}\) = 1 \(\frac{sin\theta}{cos\theta}\) = 1 \(tan \theta\) = 1 \(\theta = tan^{-1}1\) = 45^\circ

The range of wavelengths for infrared waves is given as \(10^{-3}\) m to \(10^{-6}\)m. This means that the wavelength of the radiation is longer than \(10^{-6} m\) but shorter than \{10^{-3} m\). Therefore, the only correct option is that the wavelength is longer than \(10^{-6} m\).

E = 2V, r = 0.5\Omega, I = 0.4A, P = ? E = I( R + r ) R = \(\frac{ E}{I} - r \) R = \(\frac{ 2}{0.4} - 0.5\) R = 5 - 0.5 = 4.5\Omega

Thermometer E would register the highest temperature since the hot metal is suspended from its side.

A direct current (DC) cannot pass through a parallel plate capacitor because the dielectric between the plates is non-conducting. In a parallel plate capacitor, two conductive plates are separated by a dielectric material (usually an insulator). When a voltage (potential difference) is applied across the plates, it creates an electric field between them, which stores electrical energy in the form of electric potential. The dielectric material between the plates is a non-conducting material, which means it does not allow the flow of electric current. Therefore, in a DC circuit, where current is the flow of charge over time, current cannot flow through the dielectric. Instead, the dielectric serves to store energy in the electric field between the plates without allowing the passage of charge.

The sagging of overhead electrical wires is caused by linear expansion. Linear expansion is the tendency of materials to expand in length when they are heated. When overhead electrical wires are heated by the sun, they expand and sag.

The property of a body that determines the direction of heat flow when the body is in contact with another body is the temperature. Heat naturally flows from a body at a higher temperature to a body at a lower temperature. Temperature is a measure of the average kinetic energy of the particles in a substance. When two objects at different temperatures come into contact, heat energy tends to transfer from the warmer object to the cooler one until they reach thermal equilibrium (they are at the same temperature). This is known as the second law of thermodynamics, which describes the direction of heat flow.