Radioactive Decay

Step 1: Decay Process In the decay process, the nucleus undergoes a series of transformations. Each transformation changes the atomic number and mass number. From the given information, decays into and finally . For each decay step: 1.
Alpha decay: The mass number decreases by 4, and the atomic number decreases by 2. 2.
Beta decay: The mass number remains the same, but the atomic number increases by 1. Step 2: Given Information We are given that has: - Mass number , - Atomic number . Step 3: Backtracking the Decay Process To find the mass number and atomic number of , we need to work backward through the decay process. 1. From to : - Since is formed by beta decay, the atomic number increases by 1, and the mass number remains the same. - Thus, the atomic number of is , and the mass number remains . 2. From to : - is formed by alpha decay, so the atomic number decreases by 2, and the mass number decreases by 4. - Thus, the atomic number of is , and the mass number is . 3. From to : - is formed by alpha decay, so the atomic number decreases by 2, and the mass number decreases by 4. - Thus, the atomic number of is , and the mass number is . 4. From to : - is formed by beta decay, so the atomic number increases by 1, and the mass number remains the same. - Thus, the atomic number of is , and the mass number remains . Step 4: Conclusion The mass number and atomic number of are: - , - . Thus, the correct answer is:

Concept: Activity of radioactive material: where is decay constant. Step 1: {\color{red}Relationship between and .} So: Step 2: {\color{red}Graph interpretation.} This is a linear relation passing through origin. But plotted with vs gives straight line. Step 3: {\color{red}Slope direction.} As activity decreases, nuclei decrease proportionally ⇒ straight decreasing line in plotted orientation. Correct graph: (C).

Concept: Decay rules: \begin{itemize} \item : \item : \item : no change \end{itemize} Step 1: {\color{red}Reverse steps from .} Given: Step 2: {\color{red}Undo gamma.} No change: Step 3: {\color{red}Undo alpha.} Add 4 and 2: Step 4: {\color{red}Undo beta minus.} Decrease Z by 1: Step 5: {\color{red}Undo alpha again.}