In each of the following radioactive decay processes, supply the missing particle. a. \(^{60} \mathrm{Co} \rightarrow^{60} \mathrm{Ni}+?\) b. \(^{97} \mathrm{Tc}+? \rightarrow^{97} \mathrm{Mo}\) c. \(^{99} \mathrm{Tc} \rightarrow^{99} \mathrm{Ru}+?\) d. \(^{239} \mathrm{Pu} \rightarrow^{235} \mathrm{U}+?\)

Short Answer

Expert verified
a. The missing particle is a beta particle, or an electron: \(^0_{-1}\beta\). b. The missing particle is a positron: \(^0_{+1}e\). c. The missing particle is a beta particle, or an electron: \(^0_{-1}\beta\). d. The missing particle is an alpha particle: \(^4_2\alpha\).

Step by step solution

01

Identify given values

In the given radioactive decay process, we have the following information: - The mass of the initial substance, \(^{60}\mathrm{Co}\). - The mass of the decay product, \(^{60}\mathrm{Ni}\).
02

Apply conservation laws

Using the conservation of atomic and mass numbers, we can write the following equations: - Atomic number: 27 = 28 + Z - Mass number: 60 = 60 + A From the equations above, we can calculate A and Z as: - A = 0 - Z = -1 The missing particle is an electron, also known as a beta particle, which is represented by \(^0_{-1}\beta\).
03

Answer#a.

The missing particle is a beta particle, or an electron: \(^0_{-1}\beta\). b. \(^{97} \mathrm{Tc}+? \rightarrow^{97} \mathrm{Mo}\)
04

Identify given values

In the given radioactive decay process, we have the following informations: - The mass of the initial substance, \(^{97}\mathrm{Tc}\). - The mass of the decay product, \(^{97}\mathrm{Mo}\).
05

Apply conservation laws

Now we apply the conservation laws again. - Atomic number: 43 + Z = 42 - Mass number: 97 + A = 97 From the above equations, we get A = 0 and Z = -1. This means the missing particle is a positron, represented by \(^0_{+1}e\).
06

Answer#b.

The missing particle is a positron: \(^0_{+1}e\). c. \(^{99} \mathrm{Tc} \rightarrow^{99} \mathrm{Ru}+?\)
07

Identify given values

In the given radioactive decay process, we have the following informations: - The mass of the starting substance, \(^{99}\mathrm{Tc}\). - The mass of the decay product, \(^{99}\mathrm{Ru}\).
08

Apply conservation laws

We can apply the conservation laws as follows: - Atomic number: 43 = 44 + Z - Mass number: 99 = 99 + A Solving the equations gives A = 0 and Z = -1. The missing particle is a beta particle, or an electron, represented by \(^0_{-1}\beta\).
09

Answer#c.

The missing particle is a beta particle, or an electron: \(^0_{-1}\beta\). d. \(^{239} \mathrm{Pu} \rightarrow^{235} \mathrm{U}+?\)
10

Identify given values

In the given radioactive decay process, we have the following informations: - The mass of the starting substance, \(^{239}\mathrm{Pu}\). - The mass of the decay product, \(^{235}\mathrm{U}\).
11

Apply conservation laws

For this radioactive decay process, we can write the conservation laws as follows: - Atomic number: 94 = 92 + Z - Mass number: 239 = 235 + A The calculated values for A are 4 and Z equals 2. The missing particle is an alpha particle, which is represented by \(^4_2\alpha\).
12

Answer#d.

The missing particle is an alpha particle: \(^4_2\alpha\).

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