Question

Of the two isotopes of tungsten, \({ }^{160} \mathrm{~W}\) and \({ }^{185} \mathrm{~W}\), one decays by \(\beta\) emission and one decays by \(\alpha\) emission. Which does which? Explain.

Short answer

\(^{160} \mathrm{~W}\) undergoes \( \beta \) decay, and \(^{185} \mathrm{~W}\) undergoes \( \alpha \) decay.

Step-by-step solution

Determine the Decay Type by Mass Number

An isotope undergoing \( \alpha \) decay loses two protons and two neutrons, while \( \beta \) decay involves the conversion of a neutron to a proton. Since \(^{185} \mathrm{~W} \) is heavier, \( \alpha \) decay is likely because it loses 4 atomic mass units, leading to a smaller next isotope. Lighter isotopes like \({ }^{160} \mathrm{~W} \) are often involved in \( \beta \) decay.

Check the Positions in the Periodic Table

Examine the atomic numbers: Tungsten (W) has atomic number \( Z = 74 \). After \( \alpha \) decay, the new element has \( Z-2 = 72 \), forming a stable isotope close to a known element such as Hafnium (Hf). Conversely, \( \beta \) decay will transform \(^{160} \mathrm{~W} \) into Re (Rhenium). Since Re has \( Z = 75 \), this suggests \( \beta \) decay.

Determine Stability and Path of Decay

\(^{160} \mathrm{~W} \) with \( \beta \) emission will produce \(^{160} \mathrm{~{Re}} \), known to be relatively stable. \( \alpha \) decay often happens with heavier isotopes like \(^{185} \mathrm{~W} \) to achieve a balanced neutron-proton ratio.

Key concepts

Alpha Decay

Alpha decay is a type of radioactive decay where an unstable nucleus releases an alpha particle. This particle consists of two protons and two neutrons, causing the original element to lose four units in its mass number and two in its atomic number. As a result, the element transforms into a new element that is two places back in the periodic table. For instance, when tungsten undergoes alpha decay, it produces an element like hafnium.

Alpha decay generally occurs in heavier isotopes. This is because losing four atomic mass units helps the nucleus become more stable. Heavier elements often use this decay pathway to reach a stable neutron-proton ratio and reduce the size of their massive nucleus.
- **Characteristics of Alpha Decay:** - Releases an alpha particle (2 protons, 2 neutrons) - Reduces mass number by 4 - Reduces atomic number by 2 - Occurs frequently in very heavy elements

Beta Decay

Beta decay involves transforming a neutron into a proton in the nucleus, emitting a beta particle (an electron or positron) in the process. This changes the atomic number of the element by one unit, moving it one place forward in the periodic table while the mass number remains unchanged.

In the case of tungsten isotopes, beta decay transforms the tungsten isotope into an element like rhenium. This decay process is highly dependent on the neutron-to-proton ratio. When there are too many neutrons, converting one to a proton via beta decay can stabilize the isotope.
- **Characteristics of Beta Decay:** - Converts a neutron into a proton - Emits a beta particle - Increases atomic number by 1 - Keeps the mass number unchanged

Neutron-Proton Ratio

The neutron-proton ratio is crucial for understanding nuclear stability. This ratio determines whether an isotope is likely to undergo radioactive decay. For heavier elements, a higher neutron-proton ratio is often needed for stability. However, if the ratio is too high or too low, the isotope may decay.

Alpha decay occurs when the neutron-proton ratio is not sufficient to hold the nucleus together due to its size. Conversely, beta decay can adjust the neutron-proton ratio by converting a neutron into a proton, thus balancing nuclear forces.
- **Importance of Neutron-Proton Ratio:** - Determines stability of the nucleus - Influences the type of decay - Key factor for whether beta or alpha decay will occur