During alpha decay, what happens is that a large, unstable nucleus spontaneously disintegrates to form a more stable daughter nucleus and, in the process, emits an alpha particle (alpha ray or alpha radiation). The alpha particle has two neutrons, two protons, an atomic mass of 4, and a charge of +2e (two positrons), like a helium nucleus.
Thus, α-decay changes the parent nuclide’s mass by four and atomic number by two, forming a new nuclide or element. Also, the process dissipates excess energy as kinetic energy of an alpha particle and daughter nucleus recoil.
Learn about α-decay, including its meaning, why it happens, how to write alpha decay equations, and some of its uses.
Understanding radioactive decay
Radioactive decay (radioactivity, nuclear decay, radioactive/nuclear disintegration) is the spontaneous loss of energy by unstable atomic nuclei (radionuclides) via the emission of radiation to form more stable nuclides. Radiation is the emission or transmission of energy through particles or waves through a medium or space.
The most common decay types are alpha (α), beta (β), and gamma (γ). However, others include neutron emission, electron capture, nuclear fission, and cluster decay.
Lastly, radioactive decay is stochastic (has random probability), and you cannot say which atom will next undergo decay, regardless of the length of its existence. However, it is possible to express the overall decay rate as a half-life or decay constant.
What is alpha decay (α-decay)
Alpha decay is a radioactive decay that occurs when an unstable parent nucleus disintegrates into a more stable daughter nucleus, emitting an alpha particle with a helium nucleus structure \( ^4_2He^{2+} \), i.e., two neutrons, two protons, an atomic mass of 4u and a +2e charge like helium nucleus. The symbol of the alpha decay is the lowercase Greek letter alpha α.
The resultant daughter nucleus or nuclide will have two fewer protons and neutrons and four less atomic mass than the parent nucleus, i.e., an α-decay decreases the nuclear mass of the parent nucleus by four and the atomic number by two, resulting in a new element or nuclide formation with different properties.
Therefore, alpha decay is a type of nuclear fission or a radioactive transmutation process that results in a new nuclide (daughter element) that will be more stable.
Note that the daughter nucleus can undergo further α-decay if the resultant isotope is unstable, too. Also, if in an excited state, it may emit gamma radiation to dissipate the excess energy.
Lastly, for those who want to know more, the University of Colorado Boulder has PHET alpha decay interactive alpha decay simulations, which can help you visualize what happens.
Why does an α-decay happen?
The main reason for an alpha decay is to increase the stability of the resultant daughter atomic nucleus, i.e., it creates a daughter nucleus with a lower energy state. It occurs in a large, unstable parent nucleus with a high ratio of proton to neutrons (N/Z) and forms a more stable daughter nucleus with a lower proton to neutron.
The high number of nucleons (protons and neutrons) reduces the distance between them inside the nucleus. When too close, i.e., less than 0.7 fm (femtometer), the strong nuclear forces that hold the nucleons inside the nucleus become repulsive. This, combined with the large electrostatic repulsion forces from the many protons, makes the nucleus unstable.
As a parent nucleus emits alpha radiation, its neutron-to-proton ratio will decrease. Also, the process will release energy (kinetic energy of the released particle and recoil of the daughter nucleus), something we call the Q-value or disintegration energy.
For instance, using the radium alpha decay, you will realize the parent nucleus has a Z/N ratio of 88/138 = 0.63768. In contrast, the resultant radon daughter nuclide has a proton-to-neutron ratio, i.e., Z/N of 86/136 = 0.63235. It is evident the Z/N radio decreases, and the small change will make the daughter nucleus more stable.
Historical background
While studying radiation deflection as they passed through a magnetic field, Sir Ernest Rutherford (1871 – 1937) named and distinguished alpha radiation from other radiations in 1899. Although Paul Villard, a French physicist in Paris, conducted a similar experiment, Rutherford separated radiations before he could.
In 1907, Rutherford and Thomas Royds (1884 – 1955) showed alpha particles the same as helium nuclei with two positive charges.
Later, in 1929, George Gamow, Edward Condon, and Ronald Wilfred Gurney explained the alpha decay quantum tunneling quantitatively. This theory describes how the particle escapes from the parent atomic nucleus.
Common elements that undergo alpha decay
Alpha decay is common in radionuclides (radioactive nuclei) with large nuclei, especially those whose atomic number exceeds 81 or are heavier than lead. Most of these elements are neutron-rich and include uranium-235, uranium-238, thorium-232, thorium-234, radium-226, radon-222, actinium-227, radon-198, etc. Some artificially produced alpha particle emitters include plutonium, neptunium, astatine, curium, californium, and americium.
However, some elements with atomic masses less than lead are unstable and undergo α-decay. These include heavy metals like wolfram-180, hafnium-174, osmium-186, platinum-190, and others with atomic numbers 72 (hafnium) to 81 (thallium). Also, some rare earth minerals are alpha emitters, especially the lanthanide with atomic numbers 60-71, i.e., from lanthanum to lutetium. These include neodymium-144, samarium-147, samarium-148, europium-151 and gadolinium-152.
Other are those with atomic number 52, i.e., tellurium, to atomic number 55, i.e., cesium and beryllium 8, a light element, which undergoes decay to form two alpha particles.
Alpha decay equations
You must understand how to write the α-decay equation and find the resultant daughter nucleus.
1. Writing α-decay equations or formula
When writing α-decay equations, ensure they are balanced, i.e., the net change in mass and atomic should be equal on either side. Put differently, the number of protons and neutrons before and after an alpha decay and, consequently, the mass number must be preserved.
To write the α-decay equations, we will use the standard convention of writing chemical elements and an arrow from the reactant to the products. The atomic mass A of an isotope or element and atomic number Z are written on the element symbol’s left side as subscript and superscript, respectively.
For instance, assuming X is our element symbol, the convention will be \(_Z^AX \), and an element like bismuth-210 will be written as \(_{83}^{210} Bi \).
We know that during anα-decay, the atomic mass and the atomic number of the parent nucleus will decrease by 4 and 2, respectively, to form a daughter nucleus by releasing an α-particle and energy. Assuming your parent nucleus X has atomic mass A and atomic number Z, and Y is the daughter nucleus. Then, after an α-decay, the resulting daughter nucleus Y will have a mass of (A – 4) and number (Z – 2).
Therefore, our general equation balanced nuclear equation for alpha decay will be:
\[ _Z^AX \longrightarrow _{Z – 2}^{A – 4}Y + _2^4He + Energy \]
or
\[_Z^AX \longrightarrow _{Z – 2}^{A – 4}Y + α + Energy \]
Note that α particle is equivalent to \(_2^4He \). So, we cannot write it as \(_2^4 α \).
Also, we don’t need the energy to balance our equation as it dissipates kinetic energy, and using a helium nucleus will give more visual meaning than an alpha particle. Thus, a balanced α-decay equation or formula can take the form:
\[_Z^AX \longrightarrow _{Z – 2}^{A – 4}Y + _2^4He \]
2. Finding daughter element/isotope after an alpha decay
Once you know how to write the general alpha decay equation, you can easily know which formed daughter nucleus using the periodic table. We know that the daughter nuclide will have an atomic mass of four and an atomic number of two less than the parent nuclide.
For instance, what will be the nuclide in an α-decay of uranium-234, i.e., \(_{92}^{234}U \) alpha decay?
We know uranium’s atomic mass will reduce by four and atomic number by two; you will also have an (α) particle and energy. Our alpha radiation equation will be as follows, where Y is the formed daughter nucleus:
\[_{92}^{234}U \longrightarrow _{92 – 2}^{234 – 4}Y + _2^4He \]
\[_{92}^{234}X \longrightarrow_{90}^{230}Y + _2^4He \]
To know Y, we will use a periodic table and look for an element with an atomic number of 90 and an atomic mass of 230, which happens to be thorium-230 (Th- 230). Therefore, our Y \(_{90}^{230}Th \).
This gives the nuclear equation for this decay to be:
\[_{92}^{234}X \longrightarrow_{90}^{230}Th + _2^4He \]
Examples of α-decay equations
When writing alpha decay equations, consider the exact isotope indicating its mass number, i.e., element name or symbol-mass number. For instance, uranium has many isotopes; you must state which one, like U-238 or uranium-238.
Examples of alpha decay equation following our generalized nuclear equation \(_Z^AX \longrightarrow _{Z – 2}^{A – 4}Y + _2^4He \) include the following:
1. Uranium-238 α-decay
When Uranium-238 undergoes alpha decay, it loses a mass of 4 and atomic number by two to form a daughter nuclide. The respective decay nuclear equation is \(_{92}^{238}U → _{90}^{234}Y + _2^4He \). Y is an element with a mass of 234 and an atomic number of 90; from the periodic table is thorium-234 (Th-234). Thus, the equation will be:
\[_{92}^{238}U \longrightarrow _{90}^{234}Th + _2^4He \]
2. Radium-226 α-decay
Radium (Ra) with atomic mass 226 and atomic number 88 disintegrates into daughter nuclide with atomic mass 224 and atomic number 86 by emission of an α particle. The product or daughter nuclide is radon-222 (Rn-222), and the nuclear equation for this decay is:
\[_{88}^{226}Ra \longrightarrow _{86}^{222}Rn + _2^4He \]
3. Alpha decay of americium-241
Americium (Am) is a synthetic radioactive element with an atomic mass of 241 and an atomic number of 95. Its decay equation is \(_{95}^{241}Ra \longrightarrow _{93}^{237}Y + _2^4He \). Using the periodic table, we know that Y, an element with atomic mass 93, is Neptunium-237 (Np-237). Thus, we write the final equation as follows:
\[_{95}^{241}Ra \longrightarrow _{93}^{237}Np + _2^4He \]
4. Randon-222
Randon-222, with an atomic mass of 222 and an atomic mass of 86, will undergo an α-decay by emission of an α-particle to form an element Y with an atomic mass of 218 and atomic number 84. From the periodic table, the daughter nuclide is Polonium-218 (Po-218). The nuclear disintegration equation will be:
\[_{95}^{241}Ra \longrightarrow _{93}^{237}Np + _2^4He\]5. Polonium-210 α-decay
Polonium-210, with atomic number 84 and atomic mass 210, undergoes alpha decay forming element Y with an atomic number of 206 and atomic mass of 82. We can deduce from the periodic table that the element is lead-206 (Pb-206), and the radioactivity equation is:
\[_{84}^{210}Po \longrightarrow _{82}^{206}Pb + _2^4He \]
6. Radon-198
Radon-198 (Rn-198), with atomic number 86, undergoes an alpha decay to yield polonium-194, with an atomic mass of 194 and atomic number 84. The nuclear reaction is given by:
\[_{86}^{198}Rn \longrightarrow _{84}^{194}Po + _2^4He \]
7. Alpha decay of iridium-174
Iridium-174 (Ir-174), with an atomic number of 77 and atomic mass of 174, undergoes an alpha decay to form rhenium-170 (Re-170), with an atomic mass of 170 and an atomic number of 75. Below is the equation:
\[_{77}^{174}Ir\longrightarrow _{75}^{170}Re + _2^4He \]
Alpha decay half-life
The half-life of alpha decay ranges from \(10^{-6} \) to over \( 10^{17} \) seconds and is given by the famous equation \( t_{ \frac{1} {2}} = \frac{0.693}{ \lambda} \). It correlates to the particle’s kinetic energy, i.e., the higher, the shorter the half-life.
Q-value or disintegration energy
An α-decay dissipates energy, i.e., the disintegration or Q-value equal to the kinetic energy of the emitted particle and that of the daughter nucleus recoil. It is possible to calculate the Q-value of any α-radiation applying the law of conservation of energy and momentum. See more on Q-value or alpha decay energy, including the derivation of a worked example.
Alpha decay uses
Alpha radiation helped Ernest Rutherford discover an atomic nucleus, which laid the foundation of his atomic model with a positively charged nucleus and a cloud of electrons revolving around it.
Besides this application in research, some of the everyday uses of alpha decay include the following:
1. Treating some cancers
Alpha emitter radiation therapy helps treat some cancers. For instance, targeted alpha therapy or TAT help kill cancerous cells. The process involves ingestion and -212 that then travels to the tumor site before giving off radiation that kills cancerous cells.
Also, Radium-223 is used to treat osseous metastases. Their short range effectively delivers deadly radiation only near the metastatic cells without affecting nearby tissues.
2. Alpha Particle X-Ray Spectroscopy
They are used in Alpha Particle X-ray spectroscopy (APXS), which determines rock and soil elemental composition. NASA used it in Pathfinder and Missions, including in mass, to distinguish elements in rocks on Mars.
3. Ionizing smoke detectors
Some ionizing smoke detectors use Americicium-241 as a source of alpha particles that ionize air inside the sensors. When there is smoke, it will absorb or reduce alpha particles, affecting the existing ionization and triggering an alarm.
4. Static eliminators
Some static eliminators use polonium-210 to generate alpha radiation essential in removing static electricity in equipment by ionizing air.
5. Radioisotope thermoelectric generators
Alpha particles help power radioisotope thermoelectric generators in space probes or pacemaker implants.
Frequently asked questions
Alpha particles emitted during a disintegration have low penetrative power. They can travel only a few centimeters in the air, and a sheet of paper, clothing, or the dead skin layer can block them.
Yes and No. Since the particles released have low penetrative power and short range, α-decay isn’t likely to cause harm unless inhaled or ingested. Their high ionizing power, high energy, and low penetrative power make them dangerous if inside our bodies, as they can cause DNA and tissue damage. Also, they may harm your cornea.
Therefore, always protect yourself and don’t touch materials emitting alpha particles since they often emit other more penetrating radiations like gamma and beta rays.
References
- Fenyes, T. (2011) Basic properties of the atomic nucleus. In Vértes, A., Nagy, S., Klencsár, Z., Lovas, R. G., & Rösch, F. (Eds.). Handbook of Nuclear Chemistry (2nd ed.). Springer US. https://doi.org/10.1007/978-1-4419-0720-2
- White, W. M. (2015). Isotope geochemistry. John Wiley & Sons, Inc.
- Knoll, G. (2000). Radiation detection and measurement (3rd ed.). Wiley.
- Thornton, S. T., & Rex, A. F. (2006). Modern Physics for Scientists and Engineers (3rd ed.). Thomson /Brooks/Cole.
- Lieser, K. H. (2001). Nuclear and radiochemistry fundamentals and applications (2nd ed.). Wiley-VCH.
- Choppin, G., Liljenzin, J.-O., Rydberg, J., & Ekberg, C. (2014b). Radiochemistry and nuclear chemistry (4th ed.). Elsevier.
- Takigawam, N., & Washiyama, K. (2017). Fundamentals of nuclear physics. Springer. https://doi.org/10.1007/978-4-431-55378-6