How many `alpha` and `beta`-particles are emitted in the transformation `""_(92)^(238)U rarr ""_(92)^(234)U`

Options

A. 1,1
B. 1,0
C. 1,2
D. 2,1

Answer

To determine how many alpha and beta particles are emitted in the transformation of Uranium-238 \((^{238}_{92}U)\) to Uranium-234 \((^{234}_{92}U)\), we can follow these steps:

### Step 1: Identify the initial and final states
- The initial state is Uranium-238, which has:
- Atomic number (Z) = 92
- Mass number (A) = 238
- The final state is Uranium-234, which has:
- Atomic number (Z) = 92
- Mass number (A) = 234

### Step 2: Calculate the change in mass number
- The change in mass number from \(238\) to \(234\) is:
\[ 238 - 234 = 4 \]
This indicates a loss of 4 units in mass number.

### Step 3: Determine the number of alpha particles emitted
- Each alpha particle has a mass number of 4 and an atomic number of 2. Therefore, to decrease the mass number by 4, we can emit:
\[ \text{Number of alpha particles} = \frac{4}{4} = 1 \]
So, 1 alpha particle is emitted.

### Step 4: Calculate the change in atomic number
- When 1 alpha particle is emitted, the atomic number decreases by 2:
\[ Z_{\text{final}} = Z_{\text{initial}} - 2 = 92 - 2 = 90 \]
This means after emitting 1 alpha particle, the atomic number becomes 90.

### Step 5: Determine the need for beta particles
- The final state is still Uranium (Z = 92), but after emitting 1 alpha particle, we have an atomic number of 90, which corresponds to Protactinium (Pa).
- To return to Uranium (Z = 92), we need to increase the atomic number by 2. This can be achieved by emitting beta particles.

### Step 6: Calculate the number of beta particles emitted
- Each beta particle emission increases the atomic number by 1 without changing the mass number. Therefore, to increase the atomic number from 90 to 92, we need:
\[ \text{Number of beta particles} = 2 \]

### Conclusion
- The total emissions are:
- Alpha particles: 1
- Beta particles: 2

Thus, the final answer is:
- **1 alpha particle and 2 beta particles are emitted.**