Chapter 3: Unit 4. Nuclear Reactions

Nuclear Reactions

Radioactive decay is the process by which the nucleus of an unstable atom loses energy by emitting radiation, including alpha particles, beta particles, gamma rays and positron emission or electron capture.

Most of the nuclides heavier than Lead (Pb) have been identified are radioactive. They spontaneously emit a particle, transforming themselves in the process into a different nuclide . In this section we discuss the two most common situations, the emission of an α particle (alpha decay) and the emission of an electron (beta decay).

Nuclear reaction is the conversion of one chemical element or an isotope into another chemical element. This process is also called nuclear transmutation. In an equation for a nuclear reaction, the sum of the mass numbers (A) must be equal on both sides of the equation. You can check the correctness of any of these nuclear reactions by noting that the total mass number is the same before and after the reaction; also the total atomic number is the same. Protons and neutrons are not created or destroyed; they are just shifted around. In gamma ray emission the nucleus doesn’t change, only transforms from radioactive to stable nucleus. The original nucleus before emission is called parent nucleus and the newly formed nucleus after radiation is called daughter nucleus.

Here are six fundamentally different kinds of nuclear decay reactions, and each releases a different kind of particle or energy. The essential features of each reaction are shown in Figure 20.2.1

The most common are alpha and beta decay and gamma emission, but the others are essential too.

Common Modes of Nuclear Decay

Alpha Decay

Many nuclei with mass numbers greater than 200 undergo alpha (α) decay, which results in the emission of a helium-4 nucleus as an alpha (α) particle, 42α

. The general reaction is as follows:

^A_ZX(parent)→^A−4_Z−2X′(daughter)+⁴₂α (alpha particle)

The daughter nuclide contains two fewer protons and two fewer neutrons than the parent. Thus α-particle emission produces a daughter nucleus with a mass number A − 4 and a nuclear charge Z − 2 compared to the parent nucleus. Radium-226, for example, undergoes alpha decay to form radon-222:

²²⁶₈₈Ra→²²²₈₆Rn+⁴₂He

Because nucleons are conserved in this and all other nuclear reactions, the sum of the mass numbers of the products, 222 + 4 = 226, equals the mass number of the parent. Similarly, the sum of the atomic numbers of the products, 86 + 2 = 88, equals the atomic number of the parent. Thus the nuclear equation is balanced.

Just as the total number of atoms is conserved in a chemical reaction, the total number of nucleons is conserved in a nuclear reaction.

Example: Write alpha decay of Cu-68

⁶⁸₂₉Cu → ⁴₂He + ⁶⁴₂₇Co

Beta Decay

Nuclei that contain too many neutrons often undergo beta (β) decay, in which a neutron is converted to a proton and a high-energy electron that is ejected from the nucleus as a β particle:

10nunstableneutron innucleus→11pprotonretainedby nucleus+0−1βbeta particle emitted by nucleus

The general reaction for beta decay is therefore

^A_ZX(parent)→^A_Z+1X′(daughter)+⁰₋₁β(beta particle)

Although beta decay does not change the mass number of the nucleus, it does result in an increase of +1 in the atomic number because of the addition of a proton in the daughter nucleus. Thus beta decay decreases the neutron-to-proton ratio, moving the nucleus toward the band of stable nuclei. For example, carbon-14 undergoes beta decay to form nitrogen-14:

https://phet.colorado.edu/en/simulat https://phet.colorado.edu/en/simulation/legacy/beta-decayion/legacy/beta-decay

Once again, the number of nucleons is conserved, and the charges are balanced. The parent and the daughter nuclei have the same mass number, 14, and the sum of the atomic numbers of the products is 6, which is the same as the atomic number of the carbon-14 parent.

Example: Write Beta decay of  P-18

³¹₁₅P → ⁰_-1e + ³¹₁₆S

Gamma Emission

Many nuclear decay reactions produce daughter nuclei that are in a nuclear excited state, which is similar to an atom in which an electron has been excited to a higher-energy orbital to give an electronic excited state. Just as an electron in an electronic excited state emits energy in the form of a photon when it returns to the ground state, a nucleus in an excited state releases energy in the form of a photon when it returns to the ground state. These high-energy photons are γ rays.
Gamma (γ) emission can occur virtually instantaneously, as it does in the alpha decay of uranium-238 to thorium-234, where the asterisk denotes an excited state:

²³⁸₉₂U→²³⁴₉₀Th*(excitednuclearstate) +⁴₂α−→²³⁴₉₀Th+⁰₀γ

If we disregard the decay event that created the excited nucleus, then

²³⁴₉₀Th*→²³⁴₉₀Th+⁰₀γ

or more generally,

^A_ZX*→^A_ZX+⁰₀γ

Gamma emission can also occur after a significant delay. For example, technetium-99m has a half-life of about 6 hours before emitting a γ ray to form technetium-99 (the m is for metastable). Because γ rays are energy, their emission does not affect either the mass number or the atomic number of the daughter nuclide. Gamma-ray emission is therefore the only kind of radiation that does not necessarily involve the conversion of one element to another, although it is almost always observed in conjunction with some other nuclear decay reaction. Here is an example:

²³⁸₉₂U→²³⁴₉₀Th*excited nuclear state+⁴₂α−→²³⁴₉₀Th+⁰₀γ

In general nuclear reaction of an element X can be represented in following way:

²³⁴88Th*→²³⁴88Th+⁰₀γ

 Alpha emission:

^A_ZX →    ^A-4 _Z-2Y  + ⁴₂He

                                       

Beta emission:

^A_ZX →    ^A _Z+1Y  + ⁰_-1e

Gamma emission:

                         ^A_ZX*→^A_ZX+⁰₀γ

Positron emission: The symbol of positron is ꞵ⁺. Carbon-11 isotope is a positron emitter. Symbol of positron ⁰₊₁e

¹¹₆C  → ¹¹₅B + ⁰₊₁e

In the above example, both sides of the equation have same mass numbers and atomic numbers 11 and 6 respectively.

The change in proton and neutron number is shown below with the diagram:

Here is another video on how to write nuclear equation:

Nuclear reactions are not restricted to alpha, beta or gamma radiation. Sometimes a radioactive isotope is bombarded with a neutron or another radioisotopes to produce new radioisotopes.

When one or more element is changed into two or elements it is called radioactive transmutation.

For example, in the reaction below, one nitrogen radioactive nucleus is bombarded by alpha particle to produce oxygen and hydrogen nuclei. Here also, the same rile i.e., total number of atomic number Z and total mass number A should be same on the both sides of the equation.

Find below an example of neutron bombardment:

TRY THIS OUT!

https://phet.colorado.edu/en/simulation/legacy/alpha-decay

Go to the simulation site below and click  on the single atom.

1. What is the symbol of parent nuclei( starting material)?
2. How many protons and neutrons does it have?
3. What is the daughter nucleus ( product) of the reaction?
4. How many protons and neutrns does it have?
5. What is the symbol of the radiation?
6. Write the equation for nuclear reaction.
7. How long does it take to radiate?Now Click on the custom nuclei
   1. 1. Can you identify the unknown element?
      2. Write the equation for the decay reactionhttps://phet.colorado.edu/en/simulation/legacy/beta-decay Activity:
   2. 2. Go to the simulation site above and click  on the single atom. Click on the 1 example.8) What is the symbol of parent nuclei( starting material)?
      9) How many protons and neutrons does it have?
      10) What is the daughter nucleus ( product) of the reaction?
      11) How many protons and neutrns does it have?
      12) What is the symbol of the radiation?
      13) Write the equation for nuclear reaction.
      14)How long does it take to radiate?Now Click on the custom nuclei
      3) Can you identify the unknown element?
      4) Write the equation for the decay reaction:

Questions:

1. Given the reaction: ⁶⁰₂₈Co → ⁶⁰ ₂₉Ni + ⁰_-1e, is an example of beta emission

1. True
2. False

2. Write a nuclear equation of for the decay of Iridium-192 with beta and alpha emission.

Ans: 1. a) True

2.¹⁹²₇₇Ir → ¹⁹²₇₈Pt + ⁰_-1e ( beta decay)

¹⁹²₇₇Ir → ¹⁸⁸₇₅Pt + ⁴₂He ( alpha decay)