There are four radioactive decay series called thorium `(4n)`, uranium `(4n + 2)` actinium `(4n + 3)` and neptunium `(4n + 1)` series. Neptunium series is artificial while other three series are natural. The end productsd of each radioacitve decay series have stable nuclei. All natural decay series terminate at lead but neptunium or artificial series terminate at bismuth.
The end products of uranium and actinium series are, respectively

Options

A. `Pb-206, Pb-207`
B. `Pb-206,Pb-208`
C. `Pb-207,Pb-208`
D. `Pb-206,Bi-208`

Answer

To solve the question regarding the end products of the uranium and actinium radioactive decay series, we can follow these steps:

### Step 1: Understand the decay series
The question mentions four radioactive decay series: thorium, uranium, actinium, and neptunium. Among these, thorium, uranium, and actinium are natural decay series, while neptunium is artificial. The end products of these decay series are stable nuclei.

### Step 2: Identify the end products of the natural series
According to the information provided, all natural decay series (thorium, uranium, and actinium) terminate at lead (Pb). However, the neptunium series, being artificial, terminates at bismuth (Bi).

### Step 3: Determine the specific isotopes of lead
The question specifically asks for the end products of the uranium and actinium series. To identify which isotopes of lead correspond to these series, we need to consider the mathematical expressions for each series:
- Uranium series is represented as \(4n + 2\)
- Actinium series is represented as \(4n + 3\)

### Step 4: Calculate the isotopes of lead
We need to find the isotopes of lead that correspond to these expressions:
- For the uranium series, we are looking for a lead isotope where the mass number \(A\) satisfies \(A \mod 4 = 2\).
- For the actinium series, we are looking for a lead isotope where the mass number \(A\) satisfies \(A \mod 4 = 3\).

### Step 5: Identify the isotopes of lead
The common isotopes of lead are:
- Lead-206 (Pb-206)
- Lead-207 (Pb-207)
- Lead-208 (Pb-208)

Now, we can check the mass numbers:
- For Pb-206: \(206 \mod 4 = 2\) (This corresponds to the uranium series)
- For Pb-207: \(207 \mod 4 = 3\) (This corresponds to the actinium series)

### Conclusion
Thus, the end products of the uranium and actinium series are:
- Uranium series ends at Lead-206
- Actinium series ends at Lead-207

### Final Answer
The end products of the uranium and actinium series are, respectively, Lead-206 and Lead-207.

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