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

1. During the first \(\alpha\)-decay: \[ {}^{218}_{84}A \xrightarrow{\alpha} {}^{214}_{82}A_1 \] The mass number decreases by 4, and the atomic number decreases by 2. 2. During the \(\beta^-\)-decay: \[ {}^{214}_{82}A_1 \xrightarrow{\beta^-} {}^{214}_{83}A_2 \] The mass number remains the same, and the atomic number increases by 1. 3. During the \(\gamma\)-decay: \[ {}^{214}_{83}A_2 \xrightarrow{\gamma} {}^{214}_{83}A_3 \] There is no change in the mass number or the atomic number. 4. During the second \(\alpha\)-decay: \[ {}^{214}_{83}A_3 \xrightarrow{\alpha} {}^{210}_{81}A_4 \] The mass number decreases by 4, and the atomic number decreases by 2. 5. During the \(\beta^+\)-decay: \[ {}^{210}_{81}A_4 \xrightarrow{\beta^+} {}^{210}_{80}A_5 \] The mass number remains the same, and the atomic number decreases by 1. 6. During the final \(\gamma\)-decay: \[ {}^{210}_{80}A_5 \xrightarrow{\gamma} {}^{210}_{80}A_6 \] There is no change in the mass number or the atomic number. 
Final Answer: The mass number and atomic number of \(A_6\) are: \[ \boxed{210 \, \text{and} \, 80} \]