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# Nuclear Decay

It was observed that the mass of the protons and neutrons together is more than the mass of the nucleus. This difference is called mass defect.

So where is the mass going to? Is it just vanishing in the air?

No, the mass is converted to energy, It could also be emitted in the forms of decaying rays. Nuclei undergo decay if they are unstable.The mass defect found is conserved by means of mass of the decayed components.

Einstein contributed to explain this difference to attributing it to the binding energy. Binding energy binds the protons of a nucleus together in the nucleus which would otherwise repel each other and would burst the nucleus. This information was used to harness the binding energy by breaking the nuclei. So nuclear fission was that reaction used in an atom bomb which used this tremendous energy.

Einstein gave the relationship by his famous equation

E = mc2

where m is mass converted to energy and c is speed of light.

This fission reaction is accompanied by decays. Every decaying element is characterized by a decay constant. Half life is time taken to reduce the decay activity by half of the original. The relationship between the decay constant and half life is given by

2.30 log Xo/X = kt

t1/2 = $\frac{2.303}{decay\ constant}$

 Related Calculators calculate radioactive decay half life decay calculator

## Nuclear Decay Definition

"Nuclear decay or radioactive decay is the emission of energy and matter because of change in the nucleus of atom. Such unstable elements are known as radioactive element and the process is called as radioactivity." The nuclear decay involves the emission of ionizing particles or ionizing radiation.

Hence, in nuclear decay, the parent radionuclide decay or lose energy in the form of radiation, results in the formation of different nucleus containing different numbers of nucleons which are called as daughter nuclide. The parent and daughter nuclides can be same or different chemical elements depend on the radiation emitted in decay.

• Elements like uranium, polonium, radium and thorium are radioactive in nature.
• Generally all elements having atomic number greater than 82 are radioactive in nature.
• These nuclei are unstable in nature and decay spontaneously with the emission of alpha and beta particles.
• This nuclear decay leads to the formation of new elements with different physical and chemical proprieties.

The nuclear decay follows first order kinetics i.e. the rate of the reaction depends on the concentration of one molecular species.

N = N0 e-Î»t

Where

No is the initial amount
N is the amount of radioactive substance at the time t.
Î» = Nuclear rate constant
t =Time

The half life period of the radioactive element is the time during which half the amount of a given sample of the element disintegrated. It's expressed by t1/2. While the average life time of a radioactive particles before decay is known as mean lifetime and represented as "tau".

The relation between these two time periods with decay constant is

t1/2 = $\frac{0.693}{Î»}$ and

Ï„ = $\frac{1}{Î»}$

## Nuclear Decay Equations

Some examples of nuclear decay equations are

92U238 $\rightarrow$ 90Th234 + 2He4

84Po210 $\rightarrow$ 82Pb206 +2He4

6C14 $\rightarrow$ 7N14 +-1e0

The different isotope of same element can show different type of nuclear decay and form different daughter nuclei. For example, C10 and C14 show different nuclear decay results different daughter nuclei.

Radioactive decay can occur in a continues chain reaction because of the formation of radioactive daughter nuclide which can further convert in another nucleus by loss of either an alpha particle and the decrease in atomic number by two or the loss of a beta particle and the increase in atomic number by one, then we can understand the complete radioactive decay series.

## Types of Nuclear Decay

1. Nuclear decay is the spontaneous cleavage of an atomic nucleus followed by the formation of different new element with large amount of energy. This process is also termed as transmutation.
2. This decay will continue until a new stable element is formed which cannot further disintegrate, hence not radioactive. Hence by using nuclear decay, all unstable elements want to get the neutron to proton ratio one.
3. Radioactive elements emitted certain rays which have penetrating properties just like x-rays. These rays are called as radioactive rays.
4. These radioactive radiations can be three types. Alpha, beta and gamma rays.

### Difference between alpha, beta and gamma rays

 Properties Alpha Beta Gamma Symbol $\alpha$, $\alpha$2+, He2+ e-, $\beta$- $\gamma$ Mass 6.64465675(29) x 10-27 kg 9.10938291 x 10-31 kg 0 Electric charge 2e - 1.602176565(35) x 10-19 0 Composition 2 protons, 2 neutrons One electron Electromagnetic radiation Nuclear decay Penetration power Low penetration power Medium penetration power High penetration power Relative power to ionize atom 10 1 1

On the basis of emitted radiation, nuclear decay can be five types.
1. Alpha decay
2. Beta decay
3. Positron emission
4. Electron capture
5. Gamma decay

### Alpha Decay

Alpha particles carrying two units of positive charge and four times as heavy as hydrogen atoms. Generally alpha decay takes place with those elements for which the neutron to proton ratio is less and by emission of alpha particles they try to get that ration close to one. For example; 238U, 239Pu, and 241Am.

Hence, alpha decay occurs when helium nuclei come out from the parent nucleus to form an isotope with a smaller mass. This helium nucleus is known as alpha particles.

Since alpha particle is 2He4 so the alpha decay decreases the atomic number of the atom decreases by two and the atomic mass by four. For example; alpha decay of thorium forms radium which has atomic number 88.

90Th234 $\rightarrow$ 88Ra230 +2He4
Some other example of alpha decay are,
94Pu240- $\rightarrow$ 92U236 + 2He4

### Beta Decay

When an atom decays through the emission of beta particles, it termed as beta decay. When an atom has either too many protons or large number of neutrons in its nucleus, it shows beta decay. Generally beta decay occurs with the emission of some neutrino and anti neutrino particles which are high energy elementary particles with no mass and are released for conservation of energy during the decay process.

1. Negative Beta Decay

Emission of negatively charged beta particle i.e. an electron, with an anti neutrino. Since negative beta decay is -1e0, hence the atomic number of the element increases by one, while the mass remains unchanged. For example; beta decay of tritium to forms Helium-3 by the emission of negative beta particle.

1H3 $\rightarrow$ 2He3 + -1e0 + Anti neutrino

2. Positron or Positive Beta Decay

Emission of a positively charged beta particle known as positron with a neutrino is called as positive beta decay. Due to the emission of positron, the atomic number of the element to decrease while the atomic mass remains unchanged. For example; the positron emission with carbon-11 forms boron-11.

6C11$\rightarrow$ 5B11 +1e0

3. Electron Capture

This type of nuclear reaction takes place with those atoms which have small neutron to proton ratio. Hence such type of nucleus captures an electron which reacts with neutron to form proton. For example, Beryllium-7 captures one electron to form Lithium-7.

4Be7 +-1e0 $\rightarrow$ 3Li7

### Gamma Decay

Gamma rays are highly energetic rays with neither mass nor charge. Hence gamma decay from nucleus results no change in atomic number as well as atomic mass. Generally gamma decay takes place parallel to other nuclear reactions.

Some examples of gamma decay are as follows;

66Dy152 $\rightarrow$ 66Dy152 + gamma rays

2He3 $\rightarrow$ 2He3 + Gamma rays

94Pu240 $\rightarrow$ 94Pu240 + gamma rays