Question

Consider the following radioactive decay process ${ }_{84}^{218} A \xrightarrow{\alpha} A_1 \xrightarrow{\beta^{-}}A_2 \xrightarrow{\gamma} A_3 \xrightarrow{\alpha} A_4 \xrightarrow{\beta^{+}} A_5 \xrightarrow{\gamma}A_6$ The mass number and the atomic number of $A_6$ are given by:

• A. 211 and 80
• B. 210 and 80
• C. 210 and 82
• D. 210 and 84

Answer 1

The Correct Option is B

To determine the mass number and the atomic number of \( A_6 \) in the given radioactive decay process, we need to understand each type of decay and how it affects the nucleus.

1. \({ }_{84}^{218} A \xrightarrow{\alpha} A_1\): An alpha (\( \alpha \)) particle consists of 2 protons and 2 neutrons. Thus, during an alpha decay, the atomic number decreases by 2, and the mass number decreases by 4.
   • Atomic Number: \( 84 - 2 = 82 \)
   • Mass Number: \( 218 - 4 = 214 \)
2. \(A_1 \xrightarrow{\beta^{-}} A_2\): In beta-minus (\( \beta^- \)) decay, a neutron is converted into a proton, increasing the atomic number by 1 while the mass number remains unchanged.
   • Atomic Number: \( 82 + 1 = 83 \)
   • Mass Number: \( 214 \)
3. \(A_2 \xrightarrow{\gamma} A_3\): Gamma (\( \gamma \)) decay does not change the atomic number or the mass number, as it is purely an energy release.
   • Atomic Number: \( 83 \)
   • Mass Number: \( 214 \)
4. \(A_3 \xrightarrow{\alpha} A_4\): Another alpha decay reduces both atomic and mass numbers as before.
   • Atomic Number: \( 83 - 2 = 81 \)
   • Mass Number: \( 214 - 4 = 210 \)
5. \(A_4 \xrightarrow{\beta^{+}} A_5\): In beta-plus (\( \beta^+ \)) decay, a proton is converted into a neutron, decreasing the atomic number by 1 while the mass number remains unchanged.
   • Atomic Number: \( 81 - 1 = 80 \)
   • Mass Number: \( 210 \)
6. \(A_5 \xrightarrow{\gamma} A_6\): Again, gamma decay doesn't affect the atomic or mass numbers.
   • Atomic Number: \( 80 \)
   • Mass Number: \( 210 \)

Hence, the mass number and the atomic number of \( A_6 \) are 210 and 80, respectively.

The correct answer is:

210 and 80