A radium `Ra_88^224` isotope, on emission of an `alpha`-particle gives rise to a new element whose mass number and atomic number will be:

Options

A. 220 and 86
B. 225 and 87
C. 228 and 88
D. 224 and 86

Answer

To solve the problem of determining the mass number and atomic number of the new element formed when radium-224 (`Ra_88^224`) emits an alpha particle, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the initial parameters**:
- The mass number (A) of radium-224 is 224.
- The atomic number (Z) of radium is 88.

2. **Understand alpha particle emission**:
- An alpha particle (`He_2^4`) consists of 2 protons and 2 neutrons. Therefore, when an alpha particle is emitted, the mass number decreases by 4 and the atomic number decreases by 2.

3. **Apply the changes to the mass number**:
- New mass number after emission = Initial mass number - Mass number of alpha particle
- New mass number = 224 - 4 = 220

4. **Apply the changes to the atomic number**:
- New atomic number after emission = Initial atomic number - Atomic number of alpha particle
- New atomic number = 88 - 2 = 86

5. **Determine the new element**:
- The new element formed has a mass number of 220 and an atomic number of 86.
- By referring to the periodic table, the element with atomic number 86 is radon (Rn).

### Final Answer:
- The mass number of the new element is **220**.
- The atomic number of the new element is **86**.