Chapter 10, Problem 10A.15E

Interpretation Introduction

Interpretation:

The daughter nuclides and the balanced equation for the each step of radioactive decay of the Uranium-235 have to be given.

Concept Introduction:

$\beta$emission reaction:

$\text{β}$ emission is a sub type of radioactive decay called beta decay in which a positron inside a radionucleus is converted into a neutron while releasing an electroneutrino.  Positron emission is mediated by the weak force.

  ${}_{\text{z}}{\text{X}}^{\text{A}}{\stackrel{}{\to }}_{\text{z+1}}{\text{X}}^{\text{A}}{\text{+}}_{\text{-1}}{\text{e}}^{\text{0}}$

Alpha decay reaction:

Alpha decay or $\text{ α}$-decay is a type of radioactive decay in which an atomic nucleus emits an alpha particle (helium nucleus) and thereby transforms into a different atomic nucleus with a mass number that is reduced by four and an atomic number that is reduced by two.

  ${}_{\text{z}}{\text{X}}^{{}^{\text{A}}}{\stackrel{}{\to }}_{\text{Z-2}}{\text{X}}^{\text{A-4}}{\text{+}}_{\text{2}}{\text{He}}^{\text{4}}$

Explanation of Solution

1. i. Alpha emission of Uranium-235 is,

  ${}_{\text{92}}{\text{U}}^{{}^{\text{235}}}{\stackrel{}{\to }}_{\text{90}}{\text{Th}}^{\text{231}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is thorium-231.

1. ii. Beta emission of Thorium-231 is,

  ${}_{\text{90}}{\text{Th}}^{\text{231}}{\stackrel{}{\to }}_{\text{91}}{\text{Pa}}^{\text{231}}{\text{+}}_{\text{-1}}{\text{e}}^{\text{0}}$

The daughter nucleus formed during the beta emission is protactinium-231.

1. iii. Alpha emission of protactinium-231 is,

  ${}_{\text{91}}{\text{Pa}}^{\text{231}}{\stackrel{}{\to }}_{\text{89}}{\text{Ac}}^{\text{227}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is actinium-227.

1. iv. Beta emission of actinium-227 is,

  ${}_{\text{89}}{\text{Ac}}^{\text{227}}{\stackrel{}{\to }}_{\text{90}}{\text{Th}}^{\text{227}}{\text{+}}_{\text{-1}}{\text{e}}^{\text{0}}$

The daughter nucleus formed during the beta emission is thorium-227.

1. v. Alpha emission of thorium-227 is,

  ${}_{\text{90}}{\text{Th}}^{{}^{\text{227}}}{\stackrel{}{\to }}_{\text{88}}{\text{Ra}}^{\text{223}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is Radium-223.

1. vi. Alpha emission of Radium-223 is,

  ${}_{\text{88}}{\text{Ra}}^{{}^{\text{223}}}{\stackrel{}{\to }}_{\text{86}}{\text{Rn}}^{\text{219}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is Radon-219.

1. vii. Alpha emission of Radon-219 is,

  ${}_{\text{86}}{\text{Rn}}^{{}^{\text{219}}}{\stackrel{}{\to }}_{\text{84}}{\text{Po}}^{\text{215}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is Polonium-215.

1. viii. Beta emission of Polonium-215 is,

  ${}_{\text{84}}{\text{Po}}^{\text{215}}{\stackrel{}{\to }}_{\text{85}}{\text{At}}^{\text{215}}{\text{+}}_{\text{-1}}{\text{e}}^{\text{0}}$

The daughter nucleus formed during the beta emission is Astatine-215.

1. ix. Alpha emission of Astatine-215 is,

  ${}_{\text{85}}{\text{At}}^{{}^{\text{215}}}{\stackrel{}{\to }}_{\text{83}}{\text{Bi}}^{\text{211}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is Bismuth-211.

1. x. Beta emission of Bismuth-211 is,

  ${}_{\text{83}}{\text{Bi}}^{\text{211}}{\stackrel{}{\to }}_{\text{84}}{\text{Po}}^{\text{211}}{\text{+}}_{\text{-1}}{\text{e}}^{\text{0}}$

The daughter nucleus formed during the beta emission is Polonium-211.

1. xi. Alpha emission of Polonium-211 is,

  ${}_{\text{84}}{\text{Po}}^{{}^{\text{211}}}{\stackrel{}{\to }}_{\text{82}}{\text{Pb}}^{\text{207}}{\text{+}}_{\text{2}}{\text{α}}^{\text{4}}$

The daughter nucleus formed during the alpha emission is Lead-207.