Answer the following giving reason:

(a) All the photo electrons do not eject with same kinetic energy when monochromatic light is incident on a metal surface.

(b) The saturation current in case (a) is different for different intensity.

(c) If one goes on increasing the wavelength of light incident on a metal surface, keeping its intensity constant, emission of photo electrons stop at a certain wavelength for this metal.

(a) Define 'Mass defect' and 'Binding energy' of a nucleus. Describe 'Fission process' on the basis of binding energy per nucleon.

(b) A deuteron contains a proton and a neutron and has a mass of 2.013553 u . Calculate the mass defect for it in $u$ and its energy equivalence in MeV . ( $m_p=1.007277$ u, $m_n=1.008665$ u, $\left.1 \mathrm{u}=931.5 \mathrm{MeV} / \mathrm{c}^2\right)$

(a) Draw circuit arrangement for studying $V-I$ characteristics of a $p-n$ junction diode.

(b) Show the shape of the characteristics of a diode.

(c) Mention two information that you can get from these characteristics.

A circuit consisting of a capacitor $C$, a resistor of resistance $R$ and an ideal battery of emf $V$, as shown in figure is known as $R C$ series circuit.

As soon as the circuit is completed by closing key $S_1$ (keeping $S_2$ open) charges begin to flow between the

capacitor plates and the battery terminals. The charge on the capacitor increases and consequently the potential difference $V_c(=q / C)$ across the capacitor also increases with time. When this potential difference equals the potential difference across the battery, the capacitor is fully charged $(Q=V C)$. During this process of charging, the charge $q$ on the capacitor changes with time $t$ as $q=Q \left[1-e^{-t / R C}\right]$

The charging current can be obtained by differentiating it and using $\frac{d}{d x}\left(e^{m x}\right)=m e^{m x}$

Consider the case when $R=20 \mathrm{k} \Omega, C=500 \mu \mathrm{~F}$ and $V=10$ V.

(i) The final charge on the capacitor, when key $S_1$ is closed and $S_2$ is open, is

(A) $5 \mu \mathrm{C}$

(B) 5 mC

(C) 25 mC

(D) 0.1 C

(ii) For sufficient time the key $S_1$ is closed and $S_2$ is open. Now key $S_2$ is closed and $S_1$ is open. What is the final charge on the capacitor?

(A) Zero

(B) 5 mC

(C) 2.5 mC

(D) $5 \mu \mathrm{C}$

(iii) The dimensional formula for $R C$ is

(A) $\left[M L^2 T^{-3} A^{-2}\right]$

(B) $\left[M^0 L^0 T^{-1} A^0\right]$

(C) $\left[M^{-1} L^{-2} T^4 A^2\right]$

(D) $\left[M^0 L^0 T A^0\right]$

(iv) The key $S_1$ is closed and $S_2$ is open. The value of current in the resistor after 5 seconds, is

(A) $\frac{1}{2 \sqrt{e}} \mathrm{~mA}$

(B) $\sqrt{e} \mathrm{~mA}$

(C) $\frac{1}{\sqrt{e}} \mathrm{~mA}$

(D) $\frac{1}{2 e} \mathrm{~mA}$