Chapter 20, Problem 20.4QP

Interpretation Introduction

Interpretation:

Six common types of radioactive decay and the condition typically leads to each type of decay have to be explained.

Answer to Problem 20.4QP

Six common types of radioactive decay and the typical condition that leads to each type are,

1. 1) Alpha emission: $\text{Z >83}$
2. 2) Beta emission: $\text{N/Z is too large}\text{.}$
3. 3) Positron emission: $\text{N/Z is too small}\text{.}$
4. 4) Electron capture: $\text{N/Z is too small}\text{.}$
5. 5) Gamma emission: The nucleus is in an excited state.
6. 6) Spontaneous fission: Mass number > 89

Explanation of Solution

• Alpha emission ( $\text{α}$):

An unstable nucleus emits ${}_{\text{2}}^{\text{4}}\text{He}$ nucleus or alpha particle.

Example:

${}_{\text{88}}^{\text{226}}\text{Ra}\stackrel{}{\to }{}_{\text{86}}^{\text{222}}{\text{Rn + }}_{\text{2}}^{\text{4}}\text{He}$

The product nucleus has atomic number less two than the target nucleus and the mass number less four than target nucleus.

• Beta emission ( $\text{β}$):

An unstable nucleus emits a high speed electron called beta emission.  This is the process of conversion of a neutron to proton.

${}_{\text{0}}^{\text{1}}\text{n}\stackrel{}{\to }{}_{\text{1}}^{\text{1}}{\text{p +}}_{\text{-1}}^{\text{0}}\text{e}$

Example:

${}_{\text{6}}^{\text{14}}\text{C}\stackrel{}{\to }{}_{\text{7}}^{\text{14}}{\text{N +}}_{\text{-1}}^{\text{0}}\text{e}$

Atomic number of product nucleus is one more than that of target nucleus and the mass number is remains the identical.

• Positron emission ( ${\text{β}}^{\ast }$):

An unstable nucleus emits a positron called beta emission.  In a nuclear reaction a positron denoted as ${}_{\text{1}}^{\text{0}}\text{e}$ which is identical to an electron in mass $\left({}_{\text{-1}}^{\text{0}}\text{e}\right)$ but has positive instead of negative charge.

This emission is conversion of a proton to a neutron.

${}_{\text{1}}^{\text{1}}\text{p}\stackrel{}{\to }{}_{\text{0}}^{\text{1}}{\text{n +}}_{\text{1}}^{\text{0}}\text{e}$

Example:

${}_{\text{43}}^{\text{95}}\text{Tc}\stackrel{}{\to }{}_{\text{42}}^{\text{95}}{\text{Mo +}}_{\text{1}}^{\text{0}}\text{e}$

Atomic number of product nucleus is one less than that of target nucleus and the mass number is remains the identical.

• Electron capture:

An unstable nucleus will decays by capture of an electron from interior orbital of an atom.

This emission is conversion of a proton to a neutron.

${}_{\text{1}}^{\text{1}}{\text{p +}}_{-\text{1}}^{\text{0}}\text{e}\stackrel{}{\to }{}_{\text{0}}^{\text{1}}\text{n }$

Example:

${}_{\text{14}}^{\text{40}}{\text{K+}}_{\text{-1}}^{\text{0}}\text{e}\stackrel{}{\to }{}_{\text{18}}^{\text{40}}\text{Ar }$

Atomic number of product nucleus is one less than that of target nucleus and the mass number is remains the identical.

• Gamma emission ( $\text{γ}$):

Exited nucleus of a gamma photon emits radiation corresponding with a wavelength of about ${\text{10}}^{\text{-12}}\text{m}$.

Example:

${}_{\text{43}}^{\text{99m}}\text{Tc}\stackrel{}{\to }{}_{\text{43}}^{\text{99}}{\text{Tc + }}_{\text{0}}^{\text{0}}\text{γ}$

Atomic number of product nucleus has lower energy state of the target nucleus hence the atomic number and mass number are remains identical.

• Spontaneous fission:

An unstable nucleus will decay spontaneously in which heavy nucleus has mass number greater than 89, it splits into smaller nuclei and released energy.

Example:

${}_{\text{92}}^{\text{236}}\text{U}\stackrel{}{\to }{}_{\text{39}}^{96}{\text{Y + }}_{53}^{136}{\text{I + 4}}_{\text{0}}^{\text{1}}\text{n}$

Conclusion

Types of radioactive decay and the condition typically leads to each type of decay was explained.