Nuclear Stability and Radioactivity in Modern Physics

Radioactivity-are unstable structures that decay to form other nuclides by emitting particles and electromagnetic radiation.

Three Features of Radioactivity

1. When a nucleus undergoes alpha or beta decay, its atomic number Z changes and it becomes the nucleus of a different element. Thus the elements are not immutable, although the mechanism of their transformation would hardly be recognized by an alchemist.
2. The energy liberated during radioactive decay comes from within individual nuclei without external excitation, unlike the case of atomic radiation.
3. Radioactive decay is a statistical process that obeys the laws of chance. No cause effect relationship is involved in the decay of a particular nucleus, only a certain probability per unit time.

The earlier experiments, among them Rutherford and his co-workers, distinguished three components in the radiations from radio nuclides. These components were called Alpha, Beta, and Gamma.

ACTIVITIES AND HALF-LIFE

Activity

It is the rate at which the nuclei of its constituent atoms decay. If N is the number of nuclei present in the sample at a certain time, its activity R is given by

R= -dN/dt

The minus sign is used to make R a positive since dN/dt is, of course, intrinsically negative. The SI unit of activity is named after Becquerel:

1 becquerel = 1Bq = 1 decay/s

1 curie = 1 Ci = 3.70 x 10¹⁰ decays/s = 37 Gbq

Activity Law:

R=R_oe^–λt

λ – decay constant

 

Half-life

• T1/2 is the time required for the number of remaining nuclei to decrease to one-half the original number N_o. Accordingly the half-life T_1/2 of the nuclide is 5.00 h.

T_1/2 = ln 2/λ = 0.693/λ

Radioactive Decay

N = N_oe^–λt

N – number of undecayed nuclei

t- time

λ – decay constant

N_o– number of undecayed nuclei at t=0

 

Mean Lifetime

T = T_1/2/0.693 = 1.33T_1/2

 

Radioactive Series

– A series consisting of a succession of daughter products all ultimately derived from a single parent nuclide.

 

Alpha Decay

Disintegration Energy:

Q = (m_i – m_f – m_x)c²

Alpha Particle Energy:

KE_α≈A-4/A

 

 

Beta Decay

1. The electron energies observed in the beta decay of a particular nuclide are found to very continuously from 0 to a maximum value KE_max characteristics of the nuclide.
2. When the directions of the emitted electrons and of the recoiling nuclei are observed, they are almost never exactly opposite as required for linear momentum to be conserved.
3. The spins of the neutron, proton, and electron are all ½. If beta decay involves just a neutron becoming a proton and an electron, spin is not conserved.

 

n       p + e^– + v

Gamma Decay

A nucleus can exist in states whose energies are higher than that of its ground state, just as an atom can. An excited nucleus is denoted by an asterisk after its usual symbol, for instance Sr*. Excited nuclei return to their ground states by emitting photons whose energies correspond to the energy differences between the various initial and final states in the transitions involved. The photons emitted by nuclei range in energy up to several MeV, and are traditionally called gamma rays.