Neutrino theory of beta -decay, electron capture

Neutrino theory of \(\beta\)-decay:

To explain the difficulties associated with \(\beta\) -particle emission in radioactivity pauli proposed that during \(\beta\) particle emission there is another particle called as 'neutrino' is also emitted. Neutrino is a fermion having spin angular momentum \(\hbar\).

\(_ZX^A\longrightarrow _Z+1X^A+_{-1}e^\circ+\nu+Q\)

Neutrino is a fermion having spin angular momentum \(\frac{\hbar}{2}\)

1. Energy is shared between\(\beta\)-particle and neutrino. That's why the energy of\(\beta\) -particle is less than maximum K.E (\(M_p-M_d)C^2\). This solves the conservation of energy problem.

2. Angular momentum is also shared between\(\beta\) -particles neutrino, and daughter nucleus. This solves the problem of conservation of angular momentum.

3. The linear momentum is shared among\(\beta\) -particle , neutrino and daughter nucleus in such a way that the sum of linear momentum is 0.

\(\overrightarrow P_1+\overrightarrow P_2+\overrightarrow P_3=0\)

Electron capture:

When nucleus of radio active substance pulls one of the electron in nearest orbital (K-shell or L-shell) then electron jumps into nucleus and combines with proton & there is energy of neutrino along with formation of neutron.

\(_{-1}e^0+_{+1}p^1\longrightarrow _0n^1+\nu\)

and the phenomena is known as electron capture. And the atomic number of parents atom is decreased by 1 unit & mass number remains same.

This is also known as form of \(\beta\) -decay.

Eg, \(_{30}Zn^63\longrightarrow _{29}Cu^{63}+\nu\)

Inverse\(\beta\)-decay

The absorption of a neutrino by a nucleus of a radioactive substance with the conversion of neutron into proton and emission of electron is known as inversion\(\beta\) -decay

\(\nu+_0n^1\longrightarrow _+1P^1+_-1e^0\)1}

\(\bar \nu+_1p^1\longrightarrow _0n^1+_{-1}e^0\)

Activity of a radioactive substance:

It is defined as the rate of disintegration of the atom present in the sample. It is denoted by R

We have,

\(N=N_\circ e^{-\lambda t}\)

\(\frac{dN}{dt}=(-\lambda)N_\circ e^{-\lambda t}\)

or, \(\frac{dN}{dt}=\lambda N_\circ e^{-\lambda t}\)

or, R=\lambda N_\circ e^{-\lambda t}\)

\(R=R_\circ e^{-\lambda t}\dotsm(*)\)

where, \(R_\circ\)=\lambda N_\circ= initial activity of the sample.

from equation (*) we can say that the activity of the sample decreases exponentially with the time.

\(R=\lambda(N_\circ e^{-\lambda t})\)

\(R=\lambda N\dotsm(**)\)

\(R_\circ= \lambda N_\circ\dotsm(***)\)

Dividing equation (**) by (***) we get

\(\frac{R}{R_\circ}=\frac{N}{N_\circ}\)

Biological effects of ionizing radiation:

The type of radiation absorbed is a factor in determining the biological effect of ionizing radiation on an organism. Each type of ionizing radiation has its own characteristics. Alpha particles are fairly large in size and carry a double positive charge, so they tend to travel only a short distance and do not penetrate very far into tissue if at all. However alpha particles will deposit their energy over a smaller volume (possibly only a few cells if they enter a body) and cause more damage to those few cells. Beta particles are much smaller and carry a single negative charge. They will penetrate farther into the body, which means they tend to damage more cells, but with lesser damage to each. Gamma rays and x-rays are pure energy and have no mass. They are deeply penetrating and can easily pass completely through your body, but may still interact with many atoms as they pass through. Both x-rays and gamma rays spread their energy over a larger volume, which causes less damage per collision. Of course, at very high levels of exposure they can still cause a great deal of damage to tissues. Because of their penetrating ability, they can easily reach internal organs and bones which is why large doses can be used to damage cancer tissue.

Reference:

Reviews of Modern Physics. Lancaster, P.A.: Published for the American Physical Society by the American Institute of Physics, 1952. Print.

Wehr, M. Russell, and James A. Richards. Physics of the Atom. Reading, MA: Addison-Wesley Pub., 1984. Print.

Young, Hugh D., and Roger A. Freedman. University Physics. Boston, MA: Pearson Custom, 2008. Print.

Adhikari, P.B. A Textbook of Physics. 2070 ed. Vol. II. Kathmandu: Sukunda Publication, 2070. Print.