Gamow Theory of Alpha Decay

Introduction

Gamow theory of Alpha decay explains the radioactive process of decay effectively. Elements in nature are flexible. That is, to say, it is possible to convert one element into another by various processes that are classified as nuclear reactions. For example, there is a type of nuclear reaction called nuclear decay, which occurs when the nucleus of an element is unstable and releases energy, nucleons, and/or atoms to achieve stability.

One special type of nuclear decay is alpha decay which occurs when an atomic nucleus decays into another one by releasing an alpha particle. Note that an alpha particle is a nucleus created by the binding of two protons with neutrons. It is quite similar to a Helium atom, but with a charge of +2e.

Since alpha decay process involves the release of an alpha particle, the atomic and mass numbers of the original nucleus, known as the parent nucleus, is altered. To be precise, the atomic and mass numbers reduce by 2 and 4, respectively. You should remember that alpha decay is a radioactive process. That is, energy is released in the form of radiation when it occurs.

Alpha Decay Equation

Nuclear decays can be represented in the form of equations and alpha decay is no different. The general equation of alpha decay may be stated as follows −

$$\mathrm{X_Z^A→Y_{Z-2}^{A-4}+α_2^4}$$

Here,

• X_Z^A is the original nucleus, called the parent nucleus.

• Y_Z-2^A-4 is the nucleus that the parent decays into, called the daughter nucleus.

• α₂⁴ is the alpha particle.

Understanding Q Value of Alpha Decay

The Q value of a nuclear reaction is simply the difference in kinetic energies of the reactants and the products. In the context of alpha decay, we define it as the difference in the masses of the initial nucleus and the products of the reaction, multiplied by c². That is,

$$\mathrm{Q=(m_i-m_f-m_α)×c^2}$$

Here −

• Q is the Q value of the reaction.

• m_i is the mass of the parent.

• m_f is the mass of the daughter.

• m_α is alpha particle mass.

• c represents the vacuum velocity of light.

Be very careful, though. In this definition, the masses are given in units of $\mathrm{\frac{MeV}{c^2}}$ , not in atomic mass units or SI units.

So, why is understanding Q value important? As it turns out, not all elements can undergo alpha decay. Whether alpha decay can occur depends on the Q value. Sometimes, the total mass of the final products is greater than the parent. In such a case, the Q value is negative, which corresponds to the release of energy.

On the other hand, if the initial parent nucleus is very stable, its mass will be greater than the masses of the final product and thus, the Q value would be positive. This would correspond to a non-favourable alpha decay. Therefore, using the Q value, we can determine whether an alpha decay would occur easily or not.

What are the Major Components of the Equation that Represents Alpha Decay?

The alpha decay equation is written as follows −

$$\mathrm{X_Z^A→Y_{Z-2}^{A-4}+α_2^4}$$

The major components of this equation can thus be easily defined.

• X corresponds to the parent nucleus. Usually, the parent nucleus is unstable and most of the time, alpha decay is observed for very heavy nuclei (when the mass number is greater than 200).

• Y is the daughter nucleus obtained after alpha decay. Its mass number differs from the parent by 4, and its atomic number by 2. This is usually a more stable nucleus than the parent.

• α represents the alpha particle. As we previously mentioned, it is similar to a Helium atom, but with a charge of +2e. That is, alpha particles are merely Helium nuclei.

Alpha Decay Example

Decay of Radium-226

One very common example of alpha decay is the decay of Radium-226. Radium has four isotopes, of which, Ra-226 is the most stable one with a half-life of 1600 years. It decays into Radon gas and releases ionizing radiation along with an alpha particle.

The equation representing this decay is as follows −

$$\mathrm{Ra^{226}→Rn^{222}+α^4}$$

Decay of Uranium-238

Another common example is the decay of Uranium 238 into Thorium −

$$\mathrm{U^{238}→Th^{234}+ α^4}$$

What happens in Alpha Decay?

As we know that, alpha decay is a radioactive decay process. That is, it releases energy in the form of radiation. Further, it also involves the decay of a parent nucleus. The parent nucleus is converted into a more stable daughter nucleus with a lowered number of nucleons by releasing an alpha particle. The process is accompanied by a release of energy.

Gamow Theory of Alpha Decay

The Gamow theory of alpha decay can be used to derive a relation between the half-life of the alpha decay process and the energy of the alpha particle emitted. These calculations are quantum mechanical in nature and can be arrived at using the particle in a box model for the alpha particle.

Gamow’s theory starts with the hypothesis that the daughter nucleus and the alpha particle exist before the decay event inside the parent nucleus. Due to the strong potential well created by the nucleus, it is classically impossible for the alpha particle to escape. However, quantum mechanically, there is always a probability for the particles to “tunnel” through this potential barrier.

Gamow’s theory, when solved, leads to a similar relation between the decay constant and the energy of the emission as was empirically discovered by Geiger and Nuttall. Mathematically,

$$\mathrm{log_{10}λ =-\frac{a_1 Z}{√E}+a_2}$$

• λ is the decay constant.

• Z is the atomic number of the parent.

• E is the total kinetic energy of the daughter and the alpha particle.

• a1 and a2 are constants.

Conclusion

Certain elements in nature can be converted into other elements via processes known as nuclear reactions. One type of nuclear reaction is nuclear or radioactive decay, which involves the decay of an unstable nucleus into a stabler one via the release of energy and/or nucleons. Alpha decay is a type of nuclear/radioactive decay. It occurs when a certain unstable nucleus, called the parent nucleus, decays into a stabler daughter nucleus along with the release of an alpha particle. Note that an alpha particle is similar to a Helium nucleus and carries charge +2e. The equation of alpha decay is given below −

$$\mathrm{X_Z^A→Y_{Z-2}^{A-4}+α_2^4}$$

In alpha decay, mass and atomic numbers reduce by 4 and 2, respectively.

Gamow’s theory of alpha decay supposes that the alpha particle and daughter nucleus already exist within the parent and the decay occurs by the quantum mechanical tunnelling of alpha particles from the nuclear potential. It can be used to derive a relation between the decay constant and the energy of the emission.

FAQs

1. Are alpha particles dangerous?

Alpha particles do not penetrate the human skin too much and thus, are relatively safe. However, they can damage the cornea of our eyes. Also, alpha particle emission from inside the human body can damage our organs.

2. How far do alpha particles penetrate into matter?

Alpha particles are pretty docile. Even a few centimetres thick layer of air, or a thin sheet of paper can absorb them.

3. What is the typical kinetic energy of an alpha particle?

Alpha particles travel at around 5 MeV, which corresponds to a slow speed of around 15,000 km/s, owing to their high mass.

4. What other types of nuclear decay are observed?

Most commonly, alpha, beta, and gamma decays are observed. Of these, gamma decays are the most dangerous since they only involve the release of very high energy photons.

5. What are the uses of alpha decay processes?

Americium-241 releases alpha particles and is used in smoke detectors. Alpha decay was also used as a power source in artificial pacemakers. Radium-223 is used in the treatment of bone cancer.