If three helium nuclei combine to form a carbon nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimise the energy?

If a star can convert all the He nuclei completely into oxygen nuclei. The energy released per oxygen nuclei is (Mass of the helium nucleus is 4.0026 amu and mass of oxygen nucleus is 15.9994 amu)

Binding energy per nucleons vs mass curve for nucleus is shown in the figure W,X,Y and Z are four nuclei indicated on the curve . The process that would release energy is

The mass of nucleus ._(z)X^(A) is less than the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of mass m_(1) and m_(2) only if (m_(1)+m_(2)) lt M . Also two light nuclei of massws m_(3) and m_(4) can undergo complete fusion and form a heavy nucleus of mass M ''only if (m_(3)+m_(4)) gt M ''. The masses of some neutral atoms are given in the table below. |{:(._(1)^(1)H,1.007825u,._(1)^(2)H,2.014102u,),(._(1)^(3)H,3.016050u,._(2)^(4)H,4.002603u,),(._(3)^(6)Li,6.015123u,._(3)^(7)Li,7.016004u,),(._(30)^(70)Zn,69.925325u,._(34)^(82)Se,81.916709u,),(._(64)^(152)Gd,151.91980u,._(82)^(206)Pb,205.97445u,),(._(83)^(209)Bi,208.980388u,._(84)^(210)Po,209.982876u,):}| The correct statement is

The mass of a nucleus ._(Z)^(A)X is less that the sum of the masses of (A-Z) number of neutrons and Z number of protons in the nucleus.The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass M can break into two light nuclei of masses m_(1) and m_(2) only if (m_(1)+m_(2)) lt M . Also two light nuclei of masses m_(3) and m_(4) can undergo complete fusion and form a heavy nucleus of mass M'. only if (m_(3)+m_(4)) gt M' . The masses of some neutral atoms are given in the table below: |{:(._(1)^(1)H ,1.007825u , ._(1)^(2)H,2.014102u,._(1)^(3)H,3.016050u,._(2)^(4)He,4.002603u),(._(3)^(6)Li,6.015123u,._(3)^(7)Li,7.016004u,._(30)^(70)Zn,69.925325u, ._(34)^(82)Se,81.916709u),(._(64)^(152)Gd,151.91980u,._(82)^(206)Pb,205.974455u,._(83)^(209)Bi,208.980388u,._(84)^(210)Po,209.982876u):}| Taking kinetic energy ( in KeV ) of the alpha particle, when the nucleus ._(84)^(210)P_(0) at rest undergoes alpha decay, is:

A radio nuclide with disintegration constant lambda is produced in a reactor at a constant rate alpha nuclei per second. During each decay energy E_0 is released. 20% of this energy is utilized in increasing the temperature of water. Find the increase in temperature of m mass of water in time t . Specific heat of water is s . Assume that there is no loss of energy through water surface.

Photoelectrons are emitted when 400 nm radiation is incident on a surface of work - function 1.9 eV. These photoelectrons pass through a region containing alpha -particles. A maximum energy electron combines with an alpha -particle to from a He^+ ion, emitting a single photon in this process. He^+ ions thus formed are in their fourth excited state. Find the energies in eV of the photons lying in the 2 to 4 eV range, that are likely to be emitted during and after the combination. [Take, h = 4.14xx10^(-15) eV -s]

An electron joins a helium nucleus to form He^(+) . Find the wavelength of the photon emitted in this process (in nm ) if the electron is assumed to have no kinetic energy when it combines with nucleus. Assume Bohr's model to be applicable.

In a nuclear reactor a neutron of high speed (typically 10^(7) ms^(-1) ) must be slowed to of interacting with isotope ._(92)^(235)U and causing it to fission . Show that a neutron can lose most of its kinetic energy in an elastic collision with a light nuclei like deuterium or carbon which has a mass of only a few times the neutron mass . the material making up the light nuclei , usually heavy water (D_(2)O) or graphite is called a moderator .

The neutron separation energy is defined as the energy required to remove a neutron from the nucleus. Obtain the neutron separation energies of the nuclei ""_(20)^(41)Ca and ""_(13)^(27)Al from the following data: m(""_(20)^(40)Ca) = 39.962591 u m(""_(20)^(41)Ca) = 40.962278 u m(""_(13)^(26)Al) = 25.986895 u m (""_(13)^(27)Al) = 26.981541 u .