Nuclei Test - 6...

The radio-isotope used in agriculture is:

A nucleus $$^{A}_{Z}X$$ has mass represented by $$m(A, Z)$$. If $$m_p$$ and $$m_n$$ denote the mass of proton and neutron respectively and BE the binding energy(in MeV) then.

Outside nucleus

Find Binding energy of an $$\alpha-$$particle in $$MeV$$?
$$[m_{proton}=1.007825\ amu, m_{neutron}=1.008665\ amu, m_{helium}=4.002800\ amu]$$

A neutron of kinetic energy $$65\ eV$$ collides inelastically with a singly ionized helium atom at rest. It is scattered at an angle of $$90^{\circ}$$ with respect to its original direction.
Find the allowed values of the energy of the neutron and that of the atom after the collision.
[Given : Mass of $$He\ atom = 4\times$$ (mass of neutron) Ionization energy of $$H$$ atom $$= 13. 6\ eV$$]

Nuclei of a radioactive element $$A$$ are being produced at a constant rate $$\alpha$$. The element has a decay constant $$\lambda$$. At $$t =0$$, there are $$N_{0}$$ nuclei of the element.
If $$\alpha = 2N_{0}\lambda$$, calculate the number of nuclei of $$A$$ after one half life of $$A$$, and also the limiting value of $$N$$ as $$t\rightarrow \infty$$.

A system of binary stars of masses $$m_A$$ and $$m_B$$ are moving in circular orbits of radii $$r_A$$ and $$r_B$$, respectively. If $$T_A$$ and $$T_B$$ are the time periods of masses $$m_A$$ and $$m_B$$, respectively then.

If $${M}_{o}$$ is the mass of an oxygen isotope $$ { _{ 8 }^{  }{ O } }^{ 17 },{ M }_{ P },{ M }_{ N }$$ are the masses of a proton and a neutron respectively, the nuclear binding energy of the isotope is (The speed of light is C)

Binding energies of $$ _1H^2 , _2He^4 , _{26}Fe^{56} , $$ and $$_{92}U^{235}$$ nuclie are $$2.22 Me V,28.4 MeV , 492MeV $$ and $$1786MeV$$ respectively which one of the following is more stable?

Assuming that $$200\ MeV$$ of energy is released per fission of $$_{92}U^{235}$$ atom. Find the number of fission per second ,required to release $$1\ kW$$ power.