When `._90 Th^228` transforms to `._83 Bi^212`, then the number of the emitted `alpha-`and `beta-`particle is, respectively.

Options

A. `4alpha,7beta`
B. `4alpha,1beta`
C. `8alpha,7beta`
D. `4beta,4alpha`

Answer

To solve the problem of how many alpha and beta particles are emitted when Thorium-228 transforms into Bismuth-212, we can follow these steps:

### Step 1: Write Down the Nuclear Reaction
We start with the nuclear reaction:
\[ _{90}^{228}Th \rightarrow _{83}^{212}Bi + \text{alpha and beta particles} \]

### Step 2: Determine the Change in Mass Number
The mass number of Thorium is 228 and that of Bismuth is 212. We can find the difference:
\[ \text{Change in mass number} = 228 - 212 = 16 \]

### Step 3: Understand the Contribution of Alpha Particles
An alpha particle has a mass number of 4. To find out how many alpha particles are emitted, we divide the change in mass number by the mass number of an alpha particle:
\[ \text{Number of alpha particles} = \frac{16}{4} = 4 \]

### Step 4: Determine the Change in Atomic Number
Next, we look at the atomic numbers. The atomic number of Thorium is 90 and that of Bismuth is 83. The change in atomic number is:
\[ \text{Change in atomic number} = 90 - 83 = 7 \]

### Step 5: Understand the Contribution of Beta Particles
An emitted beta particle does not change the mass number but decreases the atomic number by 1. To find out how many beta particles are emitted, we consider the change in atomic number:
- The total decrease in atomic number due to alpha particles (4 alpha particles) is:
\[ 4 \text{ (from alpha particles)} \times 2 = 8 \]
- Thus, the total atomic number after emitting 4 alpha particles would be:
\[ 90 - 8 = 82 \]
- To reach Bismuth (atomic number 83), we need to increase the atomic number by 1, which can be achieved by emitting 1 beta particle:
\[ 82 + 1 = 83 \]

### Step 6: Conclusion
Thus, the total number of emitted particles is:
- Number of alpha particles = 4
- Number of beta particles = 1

So, the final answer is:
**4 alpha particles and 1 beta particle.**