Consider the following radioactive decay process `"^(218)A_(84) →alpha A_1→ beta A_2→ yama A_3 →albha A_4 →beta^(+)A_5→gammaA_6` The mass number and the atomic number of `A_6` are given by

Options

A. 211 and 80
B. 210 and 80
C. 210 and 82
D. 10 and 84

Answer

To solve the given radioactive decay process step by step, we will analyze each decay event and determine the mass number and atomic number of the final product \( A_6 \).

### Step 1: Initial Decay
The initial element is represented as \( ^{218}A_{84} \). Here, the mass number (A) is 218, and the atomic number (Z) is 84.

### Step 2: Alpha Decay
In an alpha decay, the mass number decreases by 4 and the atomic number decreases by 2:
- Mass number: \( 218 - 4 = 214 \)
- Atomic number: \( 84 - 2 = 82 \)

Thus, after alpha decay, we have:
\[ A_1 = ^{214}A_{82} \]

### Step 3: Beta Minus Decay
In a beta minus decay, the mass number remains the same, but the atomic number increases by 1:
- Mass number: \( 214 \)
- Atomic number: \( 82 + 1 = 83 \)

Thus, after beta minus decay, we have:
\[ A_2 = ^{214}A_{83} \]

### Step 4: Gamma Decay
In gamma decay, there is no change in mass number or atomic number:
- Mass number: \( 214 \)
- Atomic number: \( 83 \)

Thus, after gamma decay, we have:
\[ A_3 = ^{214}A_{83} \]

### Step 5: Alpha Decay
Again, we have an alpha decay, which decreases the mass number by 4 and the atomic number by 2:
- Mass number: \( 214 - 4 = 210 \)
- Atomic number: \( 83 - 2 = 81 \)

Thus, after this alpha decay, we have:
\[ A_4 = ^{210}A_{81} \]

### Step 6: Beta Plus Decay
In a beta plus decay, the mass number remains the same, but the atomic number decreases by 1:
- Mass number: \( 210 \)
- Atomic number: \( 81 - 1 = 80 \)

Thus, after beta plus decay, we have:
\[ A_5 = ^{210}A_{80} \]

### Step 7: Final Gamma Decay
Finally, in gamma decay, there is no change in mass number or atomic number:
- Mass number: \( 210 \)
- Atomic number: \( 80 \)

Thus, we arrive at our final product:
\[ A_6 = ^{210}A_{80} \]

### Conclusion
The mass number and atomic number of \( A_6 \) are:
- Mass number: 210
- Atomic number: 80

### Final Answer
The mass number and atomic number of \( A_6 \) are \( 210 \) and \( 80 \), respectively.

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