The Radioactive Decay Formula is the spontaneous breakup of an atomic nucleus of a radioactive material that results in the emission of radiation from the nucleus. A parent nuclide decays in a radioactive process, while a daughter nuclide is created in the Radioactive Decay Formula.

The average number of radioactive decays per unit of time or the change in the number of radioactive nuclei present is determined by the activity of the Radioactive Decay Formula as

A = – dN/dt

A is the total activity

N is the number of particles

T = time taken for the whole activity to complete

In the years 1899 and 1900, a British physicist named Ernest Rutherford (working at McGill University in Montreal, Canada) and a French physicist named Paul Villard (working in Paris) conducted experiments on electromagnetic radiation and classified it into three types. Rutherford further classified them as alpha, beta, and gamma rays based on their penetration of matter and deflection by a magnetic field.

The Extramarks experts provide information about the three Radioactive Decay Formula below:

Alpha decay formula

Beta decay formula

Gamma decay formula

### Alpha Decay Formula

Alpha particles are charged. The most frequent type of cluster decay is +2e decay, in which the parent atom ejects a defined daughter collection of nucleons, leaving another determined product behind. Alpha decay, like other cluster decays, is fundamentally a quantum tunnelling process.

It is governed by the interaction of the nuclear force and, by extension, the electromagnetic force. Because of their relatively large mass, the electrical charge of +2e, and low velocity, alpha particles have a typical K.E. of 5 MeV. Alpha particles are highly likely to contact other atoms and lose energy, and their movement is frequently slowed by a few centimetres of air.

### Beta Decay Formula

Beta decay is a kind of Radioactive Decay Formula in which a proton is converted into a neutron or vice versa within the radioactive sample’s nucleus. Processes like beta decay and alpha decay allow the nucleus of a radioactive sample to approach as near to the ideal neutron/proton ratio as feasible. During this process, the nucleus produces a beta particle, which can be either an electron or a positron. Remember that a proton may become a neutron or a neutron can become a proton. To follow the rule of charge conservation, electrons and positrons are created. Beta-decay is caused by a weak interaction.

A Radioactive Decay Formula in which a beta ray is released from an atomic nucleus is known as beta decay. The proton in the nucleus is turned into a neutron during beta decay, and vice versa. The conversion of a proton to a neutron is known as β+ decay. Similarly, β- decay occurs when a neutron is transformed into a proton. A beta particle is released as a result of the alteration in the nucleus. When there is a β- decay, the beta particle is a high-speed electron, and when there is a β+ decay, it is a positron. Beta particles are utilised to cure diseases such as eye and bone cancer, as well as tracers.

### Gamma Decay Formula

Gamma decay is the production of extremely high-frequency electromagnetic radiation, i.e. very high energy, to stabilise the unstable nucleus. One must be well-versed in the many energy states of an atom. The Nucleus has its amount of energy. Gamma decay is the nucleus’ method of transitioning from a higher energy level to a lower energy level by emitting high-energy photons. The atom’s energy level transition energies are measured in MeV. As a result, the gamma-ray released, like x-rays, has a very high energy on the order of MeV. The sole difference between gamma rays and x-rays is that gamma rays are released from the nucleus.

t1/2=0.693/λ

Here, λ is the decay constant

### Definition of the Half-Life:

The half-life of an element is the length of time it takes for half of its specific sample to react. Furthermore, it refers to the amount of time required to reduce a specific quantity’s starting value to half. This is a popular term in nuclear physics that defines how rapidly atoms undergo the Radioactive Decay Formula.

Furthermore, it may indicate how long the atom would withstand the Radioactive Decay Formula. Furthermore, the half-life can help characterise any sort of decay, whether exponential or non-exponential. An excellent example is that the medical sciences refer to the biological half-life of medications in the human body.

Half-life refers to the length of time required for half of a certain sample to react, i.e. the time required for a given quantity to reduce its starting value to half. The Radioactive Decay Formula half-life is widely used in nuclear physics to explain the rate at which an atom decays radioactively. The half-life formula is determined by dividing 0.693 by the constant. The disintegration or decay constant is referred to here.

## Solved Example

The half-life of carbon-14 is 5.730 years. Determine the rate of carbon-14 decay.

If the half-life of 100 mg of carbon-14 is 5.730 years (t=5.730). We can employ the formula.

t ln2/λ

λ= ln2t1/2

λ=0.693/5.730

λ= 0.1209