The element with atomic number 84 and mass number 218 change to other element with atomic number 84 and mass number 214. The number of `alpha and beta`-particles emitted are respectively:

Options

A. 1, 3
B. 1, 4
C. 1, 2
D. 1, 5

Answer

To solve the problem of determining the number of alpha and beta particles emitted when an element with atomic number 84 and mass number 218 changes to another element with the same atomic number (84) and mass number 214, we can follow these steps:

### Step 1: Identify the Initial and Final States
- The initial element has:
- Atomic number (Z) = 84
- Mass number (A) = 218
- The final element has:
- Atomic number (Z) = 84
- Mass number (A) = 214

### Step 2: Determine the Change in Mass Number
- The change in mass number can be calculated as follows:
\[ \Delta A = A_{\text{initial}} - A_{\text{final}} = 218 - 214 = 4 \]
This indicates a loss of 4 units in mass number.

### Step 3: Determine the Number of Alpha Particles Emitted
- Each alpha particle emitted reduces the mass number by 4 and the atomic number by 2.
- Let \( x \) be the number of alpha particles emitted. Therefore:
\[ 4x = 4 \quad \Rightarrow \quad x = 1 \]
This means 1 alpha particle is emitted.

### Step 4: Determine the Change in Atomic Number
- Since the atomic number remains the same (84), we need to account for the emissions:
- The change in atomic number due to alpha emission is:
\[ Z_{\text{final}} = Z_{\text{initial}} - 2x + y \]
Where \( y \) is the number of beta particles emitted (which increase the atomic number by 1 each).
- Substituting the known values:
\[ 84 = 84 - 2(1) + y \]
This simplifies to:
\[ 84 = 84 - 2 + y \quad \Rightarrow \quad y = 2 \]
This means 2 beta particles are emitted.

### Conclusion
- The number of alpha particles emitted is \( 1 \).
- The number of beta particles emitted is \( 2 \).

Thus, the final answer is:
- Number of alpha particles: 1
- Number of beta particles: 2