Question

Predict whether each of the following nuclides is stable or unstable (radioactive). If the nuclide is unstable, predict the type of radioactivity you would expect it to exhibit. a. \(_{19}^{45} \mathrm{K}\) b. \(\frac{56}{26} \mathrm{Fe}\) c. \(\frac{20}{11} \mathrm{Na}\) d. \(^{194}_{81} \mathrm{TI}\)

Short answer

a. \(_{19}^{45} \mathrm{K}\) is likely unstable and would exhibit beta-minus decay. b. \(^{56}_{26} \mathrm{Fe}\) seems to be stable and would not exhibit radioactivity. c. \(^{20}_{11} \mathrm{Na}\) is likely unstable and would exhibit beta-plus decay. d. \(^{194}_{81} \mathrm{Tl}\) could be either stable or unstable, but if unstable, it would undergo alpha decay.

Step-by-step solution

a. \(_{19}^{45} \mathrm{K}\)

For potassium-45, the atomic number is 19 (protons), and the mass number is 45 (protons + neutrons). It has 26 neutrons. For nuclides with atomic numbers below 20, the ratio of neutrons to protons should be close to 1:1 for stability. In this case, the ratio is 26/19, which is higher than 1, so it is likely unstable. Since the neutron to proton ratio is too high, we would expect potassium-45 to exhibit beta-minus decay.

b. \(^{56}_{26} \mathrm{Fe}\)

For iron-56, the atomic number is 26 (protons), and the mass number is 56 (protons + neutrons). It has 30 neutrons. For a stable nuclide, the ratio of neutrons to protons should be around 1:1 at low atomic numbers and increase gradually for higher atomic numbers. The ratio for this nucleus is 30/26, which is about 1.15, so it seems stable. Since iron-56 appears to be stable, it would not exhibit radioactivity.

c. \(^{20}_{11} \mathrm{Na}\)

For sodium-20, the atomic number is 11 (protons), and the mass number is 20 (protons + neutrons). It has 9 neutrons. For nuclides with atomic numbers below 20, the ratio of neutrons to protons should be close to 1:1 for stability. The ratio for this nucleus is 9/11, which is less than 1, so it is likely unstable. Since the neutron to proton ratio is too low, we would expect sodium-20 to exhibit beta-plus decay.

d. \(^{194}_{81} \mathrm{Tl}\)

For thallium-194, the atomic number is 81 (protons), and the mass number is 194 (protons + neutrons). It has 113 neutrons. For a stable nuclide, the ratio of neutrons to protons should be around 1:1 at low atomic numbers and increase gradually for higher atomic numbers. The ratio for this nucleus is 113/81, which is about 1.4, so it could be either stable or unstable. However, since the atomic number is above 82, we would expect thallium-194 to undergo alpha decay if it is unstable.

Key concepts

Radioactive Decay

Radioactive decay is a process through which an unstable atomic nucleus loses energy by emitting radiation. This process helps an unstable nuclide become more stable. The types of radiation that can be released include alpha particles, beta particles, and gamma rays, among others. Each type of decay has its own characteristic particles and energy forms. This natural phenomenon occurs because the current arrangement of protons and neutrons in the nucleus is unstable. Understanding radioactive decay helps explain why some nuclides change into different elements over time as they reach stability.

• Alpha Decay: Emits alpha particles consisting of two protons and two neutrons.
• Beta Decay: Involves the transformation of a neutron into a proton or vice versa, emitting beta particles.
• Gamma Decay: Releases energy without changing the number of protons or neutrons.

Nuclear stability and radioactive decay are key concepts in nuclear chemistry that help in understanding why certain isotopes are radioactive while others are stable.

Neutron to Proton Ratio

The neutron to proton (n/p) ratio is a crucial factor in determining whether a nuclide is stable or unstable. A stable nucleus often has a balanced number of neutrons and protons, but as you climb the atomic number ladder, this balance shifts. The simplest rule is that for atomic numbers below 20, the ratio is close to 1:1, while for heavier elements, a larger number of neutrons are required for stability.

• If the n/p ratio is too high, expect beta-minus decay where a neutron turns into a proton.
• If the ratio is too low, it leads to beta-plus decay where a proton converts into a neutron.

For example, potassium-45 has a n/p ratio of 26/19, indicating instability and resulting in beta-minus decay. This ratio is an essential guideline for predicting nuclear stability and the type of radioactive decay a nuclide may undergo.

Beta Decay

Beta decay is a type of radioactive decay involving the transformation of a neutron to a proton, or vice versa, accompanied by the emission of a beta particle, which is essentially a high-speed electron or positron. In beta-minus decay, a neutron converts into a proton while releasing an electron and an antineutrino. On the other hand, beta-plus decay involves a proton converting into a neutron, emitting a positron and a neutrino.

• Beta-minus decay: Occurs when a nucleus has too many neutrons compared to protons. Secretly ejects an electron.
• Beta-plus decay: Happens when there are too few neutrons, expelling a positron instead.

Sodium-20 is an example of a nuclide that can undergo beta-plus decay due to its low neutron to proton ratio. Understanding beta decay is vital for comprehending how atomic nuclei adjust their composition to achieve stability.

Alpha Decay

Alpha decay is a process where an unstable nucleus releases an alpha particle, comprising two protons and two neutrons, thus reducing its atomic number by two and its mass number by four. This form of decay occurs primarily in very heavy elements, as a method of increasing stability by simplifying the nucleus. Nuclides with an atomic number greater than 82 often utilize alpha decay to manage excess mass and reach a more stable configuration.

• Heavy elements like Uranium and Thallium often undergo alpha decay.
• The emission of an alpha particle decreases the nuclear charge and mass, stabilizing the nuclide.

Thallium-194, with its high atomic number, is an example of a nuclide that might experience alpha decay if it were unstable. The process is essential for understanding the pathways through which nuclei attain stability by reducing size and complexity.