(a) Describe briefly the shell model of the nucleus. (b) Show that the average life time of the radioactive nucleus of a

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(a) Describe briefly the shell model of the nucleus.(b) Show that the average life time of the radioactive nucleus of aradioactive substance is proportional to the half life of thatradioactive substance.(c) Find the average life time of the radionuclide cobalt(55CO).Given, it decreases 4% per hour. The decayproduct is non-radioactive.(d)Show that two events appear simultaneous to an observer 'A' willnot be simultaneous to another observer 'B' which is moving withrespect to A.(e)Derive an expression for the relativistic addition ofvelocities.Calculate the velocity of an object at which its kineticenergy will be twice of its rest mass energy.(f)What is a capacitor? Calculate the capacitance of a sphericalcapacitor.(g)Derive an expression and show graphically for the growth ofcharge and current in a RC circuit for a constant emf.(h)A 25 F capacitor isconnected through a 300 ohm resistor to 50 V battery. (i) What isthe time constant of the circuit? (ii) What is the final charge qoon a capacitor plate? (iii) How long does it take for the charge ona capacitor plate to reach 0.75 q0?(i)What do you understand by magnetic force on a charged particle?Obtain an expression for the torque acting on a current carryingcoil placed in a magnetic field.(k)A coil having an area of 5 cm2 and 500 turnscarries a current of 50 A. (i) What is themagnetic dipole moment of the coil? (ii) The magnetic dipole momentof the coil is lined with an external field whose strength is 0.5T. How much work would be done by an external agent to rotate thecoil through 180°?