Problem 9 - General Chemistry: Principles and Modern Applications

Question

Supply the missing information in each of the following nuclear equations representing a radioactive decay process.(a) \(160_?\mathrm{W} \longrightarrow\\{\mathrm{Hf}+?\) (b) \(38_? \mathrm{Cl} \longrightarrow_{?}^{?} \mathrm{Ar}+?\) (c) \(^{214} ? \longrightarrow_{?}^{?} \mathrm{Po}+_{-1}^{0} \boldsymbol{\beta}\) (d) \(_{17}^{32} \mathrm{Cl} \longrightarrow_{1}^{?} ?+?\)

Step-by-Step Solution

Answer

The completed nuclear equations are: \n(a) $^{160}_{74} \mathrm{W} \longrightarrow ^{156}_{72} \mathrm{Hf} + ^{4}_{2} \mathrm{He}$ \n(b) $^{38}_{17} \mathrm{Cl} \longrightarrow ^{38}_{18} \mathrm{Ar} + _{-1}^{0}\mathrm{\beta}$\n(c) $^{214}_{85} \longrightarrow_{84}^{214} \mathrm{Po} + _{-1}^{0} \boldsymbol{\beta}$\n(d) $^{32}_{17} \mathrm{Cl} \longrightarrow_{1}^{0} \mathrm{e}+ ^{32}_{16} \mathrm{S}$

Step 1: Solve for (a)

Given the decay: $^{160}_{?} \mathrm{W} \longrightarrow \dots \mathrm{Hf}+?$, W represents Tungsten. An atomic number (the number of protons) must be supplied. For Tungsten, this number is 74. The decay product is Hf (Hafnium), and W undergoes alpha decay shedding an alpha particle (He) with atomic number 2 and mass number 4, so the equation becomes: $^{160}_{74} \mathrm{W} \longrightarrow ^{156}_{72} \mathrm{Hf} + ^{4}_{2} \mathrm{He}$.

Step 2: Solve for (b)

Given the decay: $^{38}_{?} \mathrm{Cl} \longrightarrow_{?}^{?} \mathrm{Ar}+?$, Cl represents Chlorine. An atomic number must be supplied. For Chlorine, this number is 17. The decay product is Ar (Argon), and Cl undergoes beta decay, emitting a beta particle (\( \beta \)) with atomic number -1 and mass number 0, so the equation becomes: $^{38}_{17} \mathrm{Cl} \longrightarrow ^{38}_{18} \mathrm{Ar} + _{-1}^{0}\mathrm{\beta}$.

Step 3: Solve for (c)

Given the decay: $^{214}_{?} \longrightarrow_{?}^{?} \mathrm{Po}+_{-1}^{0} \boldsymbol{\beta}$, Po is a product which is Polonium, the atomic number must be supplied. For Polonium, this number is 84. The original atom is not given, but we can infer it from the total atomic number and atomic mass. The original atom must have the same atomic mass 214 and an atomic number of 85 (since a beta particle with atomic number -1 is emitted), so the equation becomes: $^{214}_{85} \longrightarrow_{84}^{214} \mathrm{Po} + _{-1}^{0} \boldsymbol{\beta}$.

Step 4: Solve for (d)

Given the decay: $^{32}_{17} \mathrm{Cl} \longrightarrow_{1}^{?} ?+?$, Cl represents Chlorine. The decay product is not given. Given that Chlorine emits a positron (with atomic number 1 and mass number 0), the product atom must be Sulfur (S) with atomic mass 32 and atomic number 16. So, the equation becomes: $^{32}_{17} \mathrm{Cl} \longrightarrow_{1}^{0} \mathrm{e}+ ^{32}_{16} \mathrm{S}$.

Key Concepts

Radioactive Decay

Radioactive decay is a process where an unstable atomic nucleus loses energy by emitting radiation. This can include particles or electromagnetic waves. Students often encounter this concept when discussing isotopes, which are forms of the same element with different numbers of neutrons.
In nature, radioactive decay occurs at a consistent rate, known as a half-life, which is the time it takes for half of a sample of the radioactive substance to decay. This concept is crucial for understanding nuclear equations, which help depict the transformation of elements.
Key points to remember:

• Radioactive decay involves emission of particles or radiation.
• It leads to the transformation of an element into another.
• Half-life is a measure of the decay rate.

Alpha Decay

Alpha decay is a common type of radioactive decay where an unstable nucleus releases an alpha particle. An alpha particle consists of 2 protons and 2 neutrons, essentially making it a helium nucleus. This results in the reduction of both the atomic mass and atomic number of the original element.
For example, when Tungsten (W) undergoes alpha decay, it releases an alpha particle, changing into Hafnium (Hf).
Key details about alpha decay:

• Decreases the atomic number by 2.
• Decreases the atomic mass number by 4.
• Produces a new element lower in the periodic table.

Beta Decay

In beta decay, an unstable nucleus transforms by emitting a beta particle, which is a high-energy, high-speed electron or positron. When an electron is emitted, it's called beta-minus decay, whereas if a positron is emitted, it's called beta-plus decay.
During beta-minus decay, a neutron is converted into a proton, increasing the atomic number by 1, while the atomic mass remains unchanged. For instance, in Chlorine's decay to Argon, a beta particle is emitted, illustrating beta decay.
Characteristics of beta decay:

• Increases or decreases the atomic number by 1 depending on the particle.
• Does not affect the atomic mass number.
• Transforms the element into the next or previous one in the periodic table.

Positron Emission

Positron emission, a form of beta-plus decay, occurs when a proton inside the nucleus is converted into a neutron while releasing a positron. This conversion decreases the atomic number by 1, turning the element into the one just before it in the periodic table.
For example, in the decay of Chlorine to Sulfur, a positron is emitted. This process helps balance out a nucleus with too many protons, adding to stabilization.
Important points about positron emission:

• Decreases the atomic number by 1.
• Atomic mass remains the same.
• Results in a more stable nucleus.