The radioactive decay of uranium into thorium is represented by the equation:
`._(92)^(238)Urarr._(90)^(234)Th+x`
What is x ?

Options

A. an electron
B. a proton
C. an alpha particle
D. a neutron

Answer

To solve the problem of determining what \( x \) is in the radioactive decay of uranium into thorium, we can follow these steps:

### Step 1: Write down the decay equation
The decay of uranium-238 into thorium-234 can be represented as:
\[ _{92}^{238}\text{U} \rightarrow _{90}^{234}\text{Th} + x \]

### Step 2: Analyze mass numbers
In nuclear reactions, the total mass number must be conserved. This means that the mass number of uranium must equal the sum of the mass numbers of thorium and \( x \):
\[ 238 = 234 + A_x \]
where \( A_x \) is the mass number of \( x \).

### Step 3: Solve for \( A_x \)
Rearranging the equation gives:
\[ A_x = 238 - 234 = 4 \]

### Step 4: Analyze atomic numbers
Similarly, the total atomic number (number of protons) must also be conserved. The atomic number of uranium is 92, and that of thorium is 90. Thus:
\[ 92 = 90 + Z_x \]
where \( Z_x \) is the atomic number of \( x \).

### Step 5: Solve for \( Z_x \)
Rearranging this equation gives:
\[ Z_x = 92 - 90 = 2 \]

### Step 6: Identify the element \( x \)
Now we have:
- Mass number \( A_x = 4 \)
- Atomic number \( Z_x = 2 \)

The element with atomic number 2 is helium (He), and its most common isotope has a mass number of 4. Therefore, \( x \) is:
\[ x = _{2}^{4}\text{He} \]
This is known as an alpha particle.

### Conclusion
Thus, the value of \( x \) is:
\[ \text{Helium (or an alpha particle)} \quad \text{or} \quad _{2}^{4}\text{He} \]

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