Chemical Kinetics and Nuclear Chemistry

Nuclear Chemistry

Nuclear Stability

Nuclear stability is a concept that helps to identify and understand the stability of isotopes. To identify the stability of isotopes or nuclei, the ratio of neutrons (n) to protons (p) should be calculated first.

Determination of n/p ratio

For the nucleus to be stable, the ratio of neutrons to protons should be greater than one.

The nuclear stability graph helps in predicting the type of decay occurring for a particular nuclide.

1) Alpha Decay: It leads to the loss of neutrons and protons (the mass number decreases by 4 units and the atomic number decreases by 2 units). It also helps in the stabilisation of heavier isotopes having atomic number more than 83.

2) Beta Decay: A neutron is converted into a proton during the ejection of an electron. The number of neutrons decreases by 1 unit, and the number of protons increases by 1 unit. The n/p ratio decreases, thus creating a more stable nuclide. So, for nuclides with high n/p ratio (nuclides found above the band of stability), beta decay is favourable.

3) Positron Emission: The n/p ratio increases when a proton is converted into a neutron. 

4) Electron Capture: It involves the absorption of an electron of an atom by its nucleus. The electron combines with a proton, creating a new neutron. This increases the n/p ratio. So, for nuclides with low n/p ratio (nuclides found below the band of stability), positron emission or electron capture is favourable.

Types of Radioactive Decay

Radioactivity is the phenomenon of spontaneous disintegration of certain elements, with emission of active radiation. Radioactive Decay: Large nuclides are generally unstable and exist for a short time. Such nuclides undergo decay (or disintegration), which results in a different nuclide due to the emission of particles or radiation.

Types of Radioactive Decay

α-Decay

In alpha decay, the parent nucleus gets transformed into a different nucleus (daughter nucleus) by emitting an alpha particle (a helium nucleus, He24)

         XZAParent Nucleus→YZ-2A-4Daughter Nucleus+He24Helium Nucleus

The atomic mass decreases by four units.

The atomic number decreases by two units.

The new element occupies a position that is two places left to the parent element in the periodic table.

Types of Radioactive Decay

Energy released is called disintegration energy (Q):

          Q=mXZA-mYZ-2A-4-mHe24c2

          Here, mXZA is the mass of parent nuclei, mYZ-2A-4 is the mass of daughter nuclei and mHe24 is the mass of alpha particle.

β-Decay

Neutron is converted into a proton, an electron and a few particles called antineutrino.

          n → p + e + ν ¯

The electron emitted from the nucleus is called a beta particle (), and the process is known as - decay.

Types of Radioactive Decay

Atomic number increases by one unit.

Atomic mass remains the same.

          XZA→YZ+1A+β-

         Q=mXZA - mYZ+1Ac2 β+Decay

Proton is converted into a neutron, a positron and a neutrino.

          p → n + e + ν ¯

         Q=mXZA - mYZ-1A-mec2

Atomic number decreases by one unit.

Atomic mass remains the same.

Types of Radioactive Decay

K-Capture or Electron Capture

Proton of a nucleus is combined with the electron of the K-shell and gives a neutron and a neutrino. X-rays are emitted by electron capture.

          p + e → n + ν

         XZA+e→YZ-1A+ν

         Q=mXZA - mYZ-1Ac2

Gamma Decay

The electromagnetic radiation emitted in a nuclear transition is called gamma ray. Due to this, the higher energy nucleus comes down to the the lower energy nucleus. This process is known as gamma decay.

Law of Radioactive Decay

Group Displacement Law

The law of radioactive displacement is also known as the Rutherford–Soddy Rule. The law describes the chemical elements and isotopes that are created during a particular type of radioactive decay.

Law of Radioactive Decay Number of radioactive nuclei at time t = N Number of radioactive nuclei undergoing decay = dN Small interval of time = dt  dN = – λ Ndt λ is decay constant (–)ve sign shows the decrease in active nuclei. dNN=-λdt∫NoNdNN=-λ∫0tdt        [Number of active nuclei at t = 0]              lnNNo=-λt⇒t=2.303λlogNoN ⇒ ln N = log N0 – λt

Law of Radioactive Decay

 N = N0e–λt

Activity (A) of Sample:

          -dNdtgives the number of decay per unit time. It is called the activity of sample.            ∵ -dNdt = λN⇒A = λN            SI unit of activity = Becquerel (Bq) = 1 dps (disintegration per second)            Other unit of activity is curie (Ci)            1 Curie = 3.7 × 1010 Bq 

Some Important Relations in Radioactivity

Specific Activity: It is the activity per unit mass

Half-life (t1/2): It is the time taken by a radioactive nucleus to become half of its initial value.

          No2=Noe-λt1/2t1/2=ln 2λ=0.693λ

Relationship Between Activity and Half-Life

          Activity at time (t = 0) = A0           Activity at time t = A           A=Ao2t/t1/2

Average Life (tav):

          tav=1λ=t1/20.693

Some Important Relations in Radioactivity

Number of atoms of nuclides left after disintegration:

          Nt=No2n

Number of α- and β-particles after disintegration:

           U92238→Pb82206+xHe24+ye-            Here, x is the number of α-particles and y is the number of β-particles.                        Number of α-particles = x = 8             Number of β-particles = y = 6             Total steps of disintegration = x + y = 8 + 6 = 14

Some Important Relations in Radioactivity

Number of active nuclei in…