A heavy radioactive parent nucleus undergoes a decay series emitting five \alpha-particles… — JAMB UTME

A heavy radioactive parent nucleus undergoes a decay series emitting five $\alpha$ -particles and four $\beta^{-}$ -particles to form a stable daughter nucleus. What is the net change in the mass number ( $A$ ) and atomic number ( $Z$ ) of the nucleus?

Mass number decreases by $20$ , and atomic number decreases by $6$ Answer
B
Mass number decreases by $20$ , and atomic number decreases by $14$
C
Mass number decreases by $9$ , and atomic number decreases by $6$
D
Mass number decreases by $20$ , and atomic number decreases by $10$

Answer

The mass number decreases by

20

, and the atomic number decreases by

6

An alpha particle emission removes 2 protons and 2 neutrons (

^{4}_{2}\text{He}

), reducing the atomic mass number by 4 and the atomic number by 2. Five alpha emissions reduce

A

20

and

Z

10

. A beta-minus emission (

^{0}_{-1}e

) converts a neutron into a proton, leaving

A

unchanged while increasing

Z

by 1. Four beta-minus emissions increase

Z

by 4. Combining these gives a net decrease in mass number of 20 and a net decrease in atomic number of 6.

Step-by-Step Solution

Determine the change in mass number (

A

) and atomic number (

Z

) due to

\alpha

-emissions.

Each

\alpha

-particle (

^{4}_{2}\text{He}

) decreases

A

4

and

Z

2

. For

5

\alpha

-particles:

\Delta A_{\alpha} = 5 \times (-4) = -20

\Delta Z_{\alpha} = 5 \times (-2) = -10

Alpha particles consist of two protons and two neutrons.

Determine the change in mass number (

A

) and atomic number (

Z

) due to

\beta^{-}

-emissions.

Each

\beta^{-}

-particle (

^{0}_{-1}e

) leaves

A

unchanged and increases

Z

1

. For

4

\beta^{-}

-particles:

\Delta A_{\beta} = 0

\Delta Z_{\beta} = 4 \times (+1) = +4

Beta-minus decay involves a neutron converting into a proton, emitting an electron.

Sum the total changes for

A

and

Z

Net

\Delta A = -20 + 0 = -20

(decrease by

20

). Net

\Delta Z = -10 + 4 = -6

(decrease by

6

Combining independent particle emission effects yields the total net change.

Key Concept

Natural radioactive radiation emissions change nuclear composition: alpha emission (

^{4}_{2}\text{He}

) reduces

A

4

and

Z

2

, whereas beta-minus emission (

^{0}_{-1}e

) keeps

A

constant and increases

Z

1

Question

Answer

Step-by-Step Solution

Key Concept

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