In the Auger process an atom makes a transition to a lower state without emitting a photon.the excess energy is transferred to an outer electron which may be ejected by the atom.(This is called an Auger electron).Assuming the nucleus to be massive, calculate the kinetic energy of an n = 4 Auger electron emitted by Chromium by absorbing the energy from a n = 2 to n = 1 transition.

A nuclear reactor is a powerful device, wherein nuclear energy is utilised for peaceful purposes. It is based upon controlled nuclear chain reaction. The nuclear chain reaction is controlled by the use of control rods (of boron or cadmium) and moderators like heavy water, graphite, etc. The whole reactor is protected with concrete walls 2 to 2.5 metre thick, so that radiations emitted during nuclear reactions may not produce harmful effects.
Read the above passage and answer the following questions:
(i) Give any two merits of nuclear reactors.
(ii) What is radiactive waste?
(iii) Why do people often oppose the location site of a nuclear reactor? What do you suggest?

Natural radioactivity is a spontaneous and self disruptive activity exhibited by a number of heavy elements in nature. Thus a heavy element disintegrates by itself without being forced by any external agent to do so.
According to radioactive decay law, the number of atoms disintegrated per second (i.e., rate of disintegration of radioactive atoms) at any instant is directly proportional to the number of radioactive atoms actually present in the sample at that instant, i.e., \(-\frac { dN }{ dt } \propto N \ or \ R=-\frac { dN }{ dt } =\lambda N,\) where is \(\lambda \) decay constant.
Read the above passage and answer the following questions :
(i) The count rate from a radioactive sample containing \({ 10 }^{ 16 }\)  atoms is \(4\times { 10 }^{ 16 }\)  per second. What is the value of decay constant?
(ii) Name the three types of radiactive radiations. Which one of them is most penetrating?
(iii) What does radioactive decay law imply in day to day life?

Marie Curie and her teacher turned husband Pierre Curie worked hard to extract radium chloride (R_aCl₂) from uranium ore. They succeeded in 192 after a long struggle. About 0.19 g of R_aCl₂ was extracted and its radioactivity was studied. They were awarded by the noble prize, which they shared it which they shared it which they shared it with Henri Becquerel.
Read the above passage and answer following questions:
(i) What are the values shown by Marie Curie and her husband?
(ii) What do you understand by radioactivity? How the half-life period is related to the disintegration constant?
(iii) How is average-life of radioactive element related to half-life?

On the basis of Bohr's theory of H-atom, total energy of electron in a stationary orbit is given by the relation
Where, n is the number of orbits. It is clear that total energy of electron in a stationary orbit is negative which implies that electron is bound to the nucleus and is not free to leave it. The value of negative energy decreases as n increases.
Read the above p[assagr and answer the following questions:
(i) What is the total energy of electron in ground state of hydrogen atom? What does it indicate?
(ii) Why does energy required to remove an electron is smaller when atom is in any one excited state?

(a) Define the terms
(i) half life (\({ T }_{ 1/2 }\)) and
(ii) average life (\(\tau \)). Find their relationships with the decay constant ( \(\lambda \))
(b) A radioactive nucleus has a decay constant, \(\lambda\) = 0.3465 (day)^-1. How long would it take the nucleus to decay to 75% of its initial amount?

For the past some time.Arti has been observing some erratic body movement, unsteadiness and lack of aoordination in the activities of hersister Radha, who also used to complain of serve headache occasionally.Aarti suggested to her parents to get a medical check-up of Radha. The doctor throughly examined Radha and diagnosed that she has a brain tumour
(a) What,according to you,are the value displayed by Arti?
(b) How can radioisotopes help a doctor to diagnose brain tumour?

Draw the plot of binding energy per nucleon (BE/A) as a function of mass number A. Write two important conclusions that can be drawn regarding the nature of nuclear force.
Use this graph to explain the release of energy in both the processes of nuclear fusion and fission.
Write the basic nuclear process of neutron undergoing p-decay. Why is the detection of neutrinos found very difficult?

(i) Draw a schematic arrangement of Geiger-Marsden experiment showing the scattering of a-particles by a thin foil of gold. Why is it that most of the a-particles go right through the foil and only a small fraction gets scattered at large angles?
Draw the trajectory of the a-particle in the coulomb field of a nucleus. What is the Significance of impact parameter and what information can be obtained regarding the size of the nucleus?
(ii) Estimate the distance of closest approach to the nucleus (Z = 80) if a 7.7 MeV a-particle before it comes momentarily to rest and reverses its direction.

In a Geiger-Marsden experiment, calculate energy of \(\alpha \ particle\)whose distance of closest approach to the nucleus of Z = 79 is \(2.8\times { 10 }^{ -14 }m\). How will the distance of closest approach be affected when the kinetic energy of the \(\alpha \ particle\)is doubled?