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

Options

A. `2alpha and 2beta`
B. `1alpha and 2beta`
C. `1 alpha` only
D. `2beta and 2alpha`

Answer

To solve the problem of how many alpha and beta particles are emitted in the transformation of Uranium-238 (U-238) to Uranium-234 (U-234), we can follow these steps:

### Step 1: Understand the transformation
We start with Uranium-238, which has an atomic number (Z) of 92 and a mass number (A) of 238. The transformation we are looking at is:
\[ _{92}^{238}U \rightarrow _{92}^{234}U \]

### Step 2: Determine the change in mass number and atomic number
In this transformation:
- The mass number decreases from 238 to 234, indicating a decrease of 4.
- The atomic number remains the same at 92.

### Step 3: Identify the emission of alpha particles
An alpha particle (α) has a mass number of 4 and an atomic number of 2. When an alpha particle is emitted:
- The mass number decreases by 4.
- The atomic number decreases by 2.

### Step 4: Calculate the number of alpha particles emitted
To decrease the mass number from 238 to 234, we can see that:
- Emitting 1 alpha particle will decrease the mass number by 4 (from 238 to 234).
- The atomic number will decrease from 92 to 90.

Thus, after emitting 1 alpha particle:
\[ _{90}^{234}Th \] (Thorium-234)

### Step 5: Identify the need for beta particles
Now, we have Thorium-234 (Th-234) with an atomic number of 90. To convert this back to Uranium (U), we need to increase the atomic number back to 92:
- We can achieve this by emitting beta particles (β).

### Step 6: Calculate the number of beta particles emitted
A beta minus particle (β-) has no mass and increases the atomic number by 1. To go from atomic number 90 (Th) to 92 (U), we need to emit 2 beta particles:
1. After 1 beta emission:
\[ _{91}^{234}Pa \] (Protactinium-234)
2. After another beta emission:
\[ _{92}^{234}U \] (Uranium-234)

### Conclusion
In total, we have:
- 1 alpha particle emitted
- 2 beta particles emitted

Thus, the answer to the question is:
**1 alpha particle and 2 beta particles.**