An n-channel silicon JFET has donor concentration of 2 \times 10^{21}/\text{m}^3 and a channel width of 4~\mu\text{m}. If the dielectric constant of silicon is 12, find the pinch-off voltage. If the FET operates with a gate-source voltage of -2~\text{V}, what is the saturation voltage V_{\text{Dsat}}?
A transistor having \alpha = 0\cdot 975 and a reverse saturation current I_{\text{CO}} = 10~\mu\text{A} is operated in CE configuration. What is \beta for this configuration? If the base current is 250~\mu\text{A}, calculate the emitter current and the collector current.
Describe briefly the construction of an enhancement type MOSFET using a p-type silicon bar. Point out the structural difference between enhancement and depletion forms of the MOSFET.
Obtain the Boolean expression for the output Y in the given logic circuit :
Simplify the expression and show that the circuit is equivalent to an AND gate with inputs A and B.
Consider a face-centred cubic lattice of side a. Deduce –
(i) The primitive translation vectors;
(ii) The volume of the primitive cell;
(iii) The reciprocal primitive translation vectors;
(iv) The volume of the reciprocal lattice
Stable light nuclei have equal number of protons and neutrons, whereas heavy nuclei have excess of neutrons. Explain why.
For a system consisting of one proton and one neutron (not necessarily a deuteron), write down the various possible states specifying clearly its isospin, spin and orbital quantum numbers.
Explain the various methods of finding the size of the nucleus. How will you determine the nuclear radius from the observation of beta rays resulting from nuclear transition when the initial and final nuclei are mirror nuclei?
By applying the conservation laws, state about the following decay equations, whether they are allowed or not allowed :
(i) \Sigma^+ \rightarrow p + \pi^0
(ii) \Sigma^0 \rightarrow \Lambda^0 + \gamma
(iii) \Lambda^0 \rightarrow n + \pi^0
On the basis of liquid-drop model, write the semi-empirical mass formula for the total binding energy. Also explain their each term.
Calculate the decay rate of {}^{14}\text{C} per gram of carbon in a living organism, assuming the ratio {}^{14}\text{C} / ^{12}\text{C} = 1\cdot 35 \times 10^{-12}. The half-life of {}^{14}\text{C} is 5730 years.
Explain the salient features of nuclear shell model. What are the magic numbers? Write the experimental facts in support of shell model of nuclei.
Given that the single particle energy separation between 1d_{5/2} and 1d_{3/2} in {}^{17}\mathrm{O} is 5\,\mathrm{MeV}. Calculate the strength of spin-orbit interaction. It is observed that 1d_{5/2} level is lower than 1d_{3/2} level.
What are the properties of the particles made up of the following quarks? Also write the names of particles :
(i) u\bar{d}
(ii) \bar{u}d
(iii) dds
(iv) uss
Why is it not possible to detect the parity violation in weak interaction by observing only the beta decay rate? Justify your answer.
What do you understand by the reproduction factor of a fission reactor? What is the maximum value of the reproduction factor in a uranium fission reaction?
In the following nuclear reactions, what particles are possible for the unknown particle X?
(i) \pi^- + p \rightarrow K^0 + X
(ii) p + p \rightarrow \pi^+ + n + \Lambda^0 + X
Assuming equal masses for up (u) and down (d) quarks, find the ratio (\mu_n/\mu_p) of the magnetic moments of neutron and proton.
Explain the origin of the nuclear magnetic moment. Deduce expression for the magnetic dipole moment with the help of the Schmidt single particle model.
Why are Raman active vibrations and IR vibrations in \mathrm{CO}_2 molecule complementary to each other?
