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 starting isotope and the end product: isotope of actinium series are

Options

A. `._(88)Ac^(227)` and `._(82)Pb^(208)`
B. `._(92)U^(235)` and `._(82)Pb^(207)`
C. `._(92)U^(238)` and `._(82)Pb^(207)`
D. `._(92)U^(235)` and `._(82)Pb^(208)`

Answer

To solve the question regarding the starting isotope and the end product of the actinium series, we will follow these steps:

### Step 1: Understand the Actinium Series
The actinium series is represented by the formula \(4n + 3\), where \(n\) is a non-negative integer. This means that the mass number of isotopes in this series, when divided by 4, will leave a remainder of 3.

### Step 2: Identify the End Product
According to the information provided, the natural decay series, including the actinium series, terminates at lead (Pb). Therefore, the end product of the actinium series is lead.

### Step 3: Determine the Isotope of Actinium
We need to find a starting isotope that fits the \(4n + 3\) condition. We can check the mass numbers of known isotopes to find one that gives a remainder of 3 when divided by 4.

### Step 4: Check Uranium-235
Let's check uranium-235 (U-235):
- Mass number = 235
- When we divide 235 by 4, we get:
\[ 235 \div 4 = 58 \quad \text{(remainder 3)} \]
Since the remainder is 3, U-235 is indeed part of the actinium series.

### Step 5: Identify the End Product Isotope
The end product of the actinium series is lead. The stable isotope of lead that we consider is lead-207 (Pb-207).

### Conclusion
Thus, the starting isotope of the actinium series is uranium-235 (U-235), and the end product is lead-207 (Pb-207).

### Final Answer
- Starting Isotope: Uranium-235 (U-235)
- End Product: Lead-207 (Pb-207)

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