An element` X` decays , first by positron emission and then two `alpha`-particles are emitted in successive radiactive decay. If the product nucleus has a mass number `229` and atomic number `89`, the mass number and atomic number of element ` X` are.

Options

A. `237,93`
B. `237,94`
C. `221,84`
D. `237,92`

Explanation

To find the mass number and atomic number of element X, we will follow the decay process step by step.

### Step 1: Identify the product nucleus
The question states that the product nucleus has a mass number of 229 and an atomic number of 89. Let's denote this product nucleus as P.

- Mass number of P (A_P) = 229
- Atomic number of P (Z_P) = 89

### Step 2: Understand the decay process
The decay process involves two steps:
1. **Positron emission**: This process decreases the atomic number by 1 (since a positron is emitted, which is equivalent to the emission of a proton).
2. **Alpha particle emission**: Each alpha particle emission decreases the mass number by 4 and the atomic number by 2. Since two alpha particles are emitted, the total decrease in mass number and atomic number will be:
- Mass number decreases by 2 * 4 = 8
- Atomic number decreases by 2 * 2 = 4

### Step 3: Backtrack the changes due to alpha particle emission
Before the emission of the two alpha particles, the mass number (A) and atomic number (Z) of the nucleus (let's call it M) before the alpha decay can be calculated as follows:

- Mass number of M (A_M) = A_P + 8 = 229 + 8 = 237
- Atomic number of M (Z_M) = Z_P + 4 = 89 + 4 = 93

### Step 4: Backtrack the changes due to positron emission
Now, we need to account for the positron emission. The positron emission decreases the atomic number by 1. Therefore, the mass number and atomic number of the original element X can be calculated as follows:

- Mass number of X (A_X) = A_M = 237 (remains unchanged during positron emission)
- Atomic number of X (Z_X) = Z_M + 1 = 93 + 1 = 94

### Conclusion
Thus, the mass number and atomic number of element X are:
- Mass number (A_X) = 237
- Atomic number (Z_X) = 94

### Final Answer:
- Mass number of element X = 237
- Atomic number of element X = 94

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