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 but mass number 214, we can follow these steps:

### Step 1: Understand the emission of alpha and beta particles
- **Alpha emission**: When an alpha particle (which consists of 2 protons and 2 neutrons) is emitted, the atomic number decreases by 2 and the mass number decreases by 4.
- **Beta emission**: When a beta particle (an electron) is emitted, the atomic number increases by 1, while the mass number remains unchanged.

### Step 2: Set up the equations
Let:
- \( X \) = number of alpha particles emitted
- \( Y \) = number of beta particles emitted

The initial element has:
- Atomic number (Z) = 84
- Mass number (A) = 218

After the emissions, the new element has:
- Atomic number (Z) = 84
- Mass number (A) = 214

### Step 3: Write the equations for mass number and atomic number
1. For mass number:
\[ 218 - 4X = 214 \]
Simplifying this gives:
\[ 4X = 4 \implies X = 1 \]

2. For atomic number:
The initial atomic number is 84. After emitting \( X \) alpha particles and \( Y \) beta particles, the equation becomes:
\[ 84 - 2X + Y = 84 \]
Simplifying this gives:
\[ -2X + Y = 0 \implies Y = 2X \]
Substituting \( X = 1 \):
\[ Y = 2(1) = 2 \]

### Step 4: Conclusion
Thus, the number of alpha particles emitted is \( X = 1 \) and the number of beta particles emitted is \( Y = 2 \).

### Final Answer
The number of alpha and beta particles emitted are respectively: **1 and 2**.

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