Physics NCERT Exemplar Solutions Class 12th Chapter Thirteen Nuclei

Consider a radioactive nucleus A which decays to a stable nucleus C through the following sequence:

                                                                                   A -> B -> C

Here B is an intermediate nuclei which is also radioactive. Considering that there are N₀ atoms of A initially, plot the graph showing the variation of number of atoms of A and B versus time.

A piece of wood from the ruins of an ancient building was found to have a ¹⁴ C activity of 12 disintegrations per minute per gram of its carbon content. The ¹⁴ C activity of the living wood is 16 disintegrations per minute per gram. How long ago did the tree, from which the wooden sample came, die? Given half-life of  ¹⁴ C is 5760 yr.

Sometimes a radioactive nucleus decays into a nucleus which itself is radioactive. An example is

³⁸sulphur $\stackrel{\mathit{h}\mathit{a}\mathit{l}\mathit{f}\mathit{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}}{\to }$ ³⁸Cl $\stackrel{\mathit{h}\mathit{a}\mathit{l}\mathit{f}\mathit{}\mathit{l}\mathit{i}\mathit{f}\mathit{e}}{\to }$ 38Ar(stable)

Assume that we start 1000 ³⁸S nuclei at time t=0. The number of ³⁸Cl is of count zero at t=0 and will be again zero at t= $\mathit{\infty }$  at what value of t, would the number of counts be a a maximum?

Deuteron is a bound state of a neutron and a proton with a binding energy B = 2.2 MeV. A γ-ray of energy E is aimed at a deuteron nucleus to try to break it into a (neutron + proton) such that the n and p move in the direction of the incident γ-ray. If  E = B, show that this cannot happen. Hence, calculate how much bigger than B must be E be for such a process to happen.

The deuteron is bound by nuclear forces just as H-atom is made up of p and e bound by electrostatic forces. If we consider the force between neutron and proton in a deuteron as given in the form a coulomb potential but with an effective charge e’.

F= ke’²/r estimate the value of e’/e given that the the binding energy of a duetron is 2.2MeV.

Suppose we consider a large number of containers each containing initially 10000 atoms of a radioactive material with a half life of 1 year. After 1 year,
(a) All the containers will have 5000 atoms of the material
(b) All the containers will contain the same number of atoms of the material but that number will only be approximately 5000
(c) The containers will in general have different numbers of the atoms of the material but their average will be close to 5000
(d) None of the containers can have more than 5000 atoms

The gravitational force between a H atom and a another particle of mass m will be given newton’s law

F=GMm/r² where r in km

(a) M=m_proton+m_electron

(b) M=m_proton+m_electron-

(c) M is not relate to the mass of the hydrogen atom

(d) M=m_proton+m_electron-(|V|)= magnitude of the potential energy of electron in H atom.

When a nucleus in an atom undergoes a radioactive decay, the electronic energy levels of the atom
(a) Do not change for any type of radioactivity
(b) Change for α and β-radioactivity but not for γ-radioactivity
(c) Change for α -radioactivity but not for others
(d) Change for β-radioactivity but not for others

Two projectiles are thrown with same initial velocity making an angle of $45°$ and $30°$ with the horizontal respectively. The ration of their respectively ranges will be:

In a Vernier Calipers, 10 divisions of Vernier scale is equal to the 9 divisions of main scale. Then both jaws of Vernier calipers touch each other, the zero of the Vernier scale is shifted to the left of zero of the main scale and 4^th Vernier scale division exactly coincides with the main scale reading. One main scale division is equal to 1mm. While measuring diameter of a spherical body, the body is held between two jaws. It is now observed that zero of the Vernier scale lies between 30 and 31 divisions of main scale reading and 6^th Vernier scale division exactly coincides with the main scale reading. The diameter of the spherical body will be:

A ball of mass 0.15 kg hits the wall with its initial speed of 12 ms^-1and bounces back without changing its initial speed. If the force applied by the wall on the ball during the contact is 100 N, calculate the time during of the contact of ball with the wall.

In a meter bridge experiment, for measuring unknown resistance ‘S’, the null point is obtained at a distance 30cm from the left side as shown at point D. If R is 5.6 $k\Omega$ , then the value of unknown resistance ‘S’ will be ___________ $\Omega .$

The one division of main scale of Vernier calipers reads 1mm and 10 divisions of Vernier scale is equal to the 9 divisions on main scale, When the two jaws of the instrument touch each other, the zero of the Vernier lies to the right of zero of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the zero of the Vernier scale lies in between 4.1 cm and 4.2cm and 6^th Vernier division coincides with a main scale division. The diameter of the bob will be ________× 10^-2 cm.

Two beams of light having intensities I and 4I interfere to produce a fringe pattern on a screen. The phase difference between the two beams are p/2 and p/3 at points A and B respectively. The difference between the resultant intensities at the two points is xI. The value of x will be________.