Chapter 14, Problem 14.12PAE

(a)

Interpretation Introduction

To determine:

The complete equation for the given radioactive decay and identify the missing particle

$Be+?\stackrel{}{\to }Li+He$

Explanation of Solution

Because this is an alpha decay, the helium nucleus is ejected with decrease in mass number by 4 and atomic number by 2 of the parent nucleus. By balancing the mass numbers of products with that of parent nuclei, the mass number of missing particle is $6+4-9=1$. Similarly, atomic number of the missing particle is $3+2-4=1$. The nucleus of atomic number 1 is Hydrogen. Hence, the equation is:

$Be+H\stackrel{}{\to }Li+He$

(b)

Interpretation Introduction

To determine:

The complete equation for the given radioactive decay and identify the missing particle

$?+n\stackrel{}{\to }Na+He$

Explanation of Solution

In case of alpha decay, the helium nucleus is ejected. By balancing the mass numbers of products with that of a parent nuclei, the mass number of missing particle is $24+4-1=27$. Similarly, atomic number of the missing particle is $11+2-0=13$. The nucleus of atomic number 13 is Aluminum. Hence, the equation is:

$Al+n\stackrel{}{\to }Na+He$

(c)

Interpretation Introduction

To determine:

The complete equation for the given radioactive decay and identify the missing particle:

$Ca+?\stackrel{}{\to }K+H$

Explanation of Solution

In the given equation, balancing the mass number and atomic number of the product and reactant sides, we get, the mass number of missing particle is $40+1-40=1$. Similarly, atomic number of the missing particle is $19+1-20=0$. The particle with atomic number 0 and mass number 1 is Neutron. Hence, the equation is:

$Ca+n\stackrel{}{\to }K+H$

(d)

Interpretation Introduction

To determine:

The complete equation for the given radioactive decay and identify the missing particle

$Am+He\stackrel{}{\to }Bk+?$

Explanation of Solution

By balancing the mass numbers of products with that of parent nuclei, the mass number of missing particle is $241+4-243=2$. Similarly, atomic number of the missing particle is $95+2-97=0$. The particle with 0 mass number is neutron. Hence, the equation is:

$Am+He\stackrel{}{\to }Bk+2n$

(e)

Interpretation Introduction

To determine:

The complete equation for the given radioactive decay and identify the missing particle

$Cm+C\stackrel{}{\to }4n+?$

Explanation of Solution

In case of neutron decay, the mass number gets reduced. By balancing the mass numbers of products with that of parent nuclei, the mass number of missing particle is $246+12-4\times 1=254$. Similarly, atomic number of the missing particle is $96+6-4\times 0=102$. The nucleus of atomic number 102 is Nobelium. Hence, the equation is:

$Cm+C\stackrel{}{\to }4n+No$

(f)

Interpretation Introduction

To determine:

The complete equation for the given radioactive decay and identify the missing particle:

$U+?\stackrel{}{\to }Fm+5n$

Explanation of Solution

In the given equation, balancing the mass number and atomic number of the product and reactant sides, we get, the mass number of missing particle is $249+5\times 1-238=16$. Similarly, atomic number of the missing particle is $100+5\times 0-92=8$. The nucleus with atomic number 8 is Oxygen. Hence, the equation is:

$U+O\stackrel{}{\to }Fm+5n$

Conclusion

Therefore, if one of the species from the radioactive decay equation is missing, it can be determined by balancing atomic numbers and atomic mass numbers.