Consider the following nuclear reactions
`._(92)^(238)M rarr ._(X)^(Y)N + 2alpha, ._(X)^(Y)N rarr ._(B)^(A)L + 2beta`
The number of neutrons in the element L is

Options

A. 142
B. 144
C. 140
D. 146

Explanation

To solve the problem, we need to analyze the given nuclear reactions step by step.

### Step 1: Analyze the first reaction
The first reaction is:
\[ _{92}^{238}M \rightarrow _{X}^{Y}N + 2\alpha \]
Here, \(M\) (which is Uranium-238) decays into element \(N\) and emits 2 alpha particles. Each alpha particle consists of 2 protons and 2 neutrons.

### Step 2: Determine the mass and atomic numbers after the decay
- The mass number of \(M\) is 238, and it emits 2 alpha particles, each with a mass number of 4.
- Therefore, the total mass number lost due to the emission of 2 alpha particles is \(2 \times 4 = 8\).
- The new mass number \(Y\) for element \(N\) can be calculated as:
\[ Y = 238 - 8 = 230 \]
- The atomic number of \(M\) is 92, and it loses 4 protons (2 from each alpha particle).
- Therefore, the new atomic number \(X\) for element \(N\) is:
\[ X = 92 - 4 = 88 \]

Thus, the first reaction can be rewritten as:
\[ _{92}^{238}M \rightarrow _{88}^{230}N + 2\alpha \]

### Step 3: Analyze the second reaction
The second reaction is:
\[ _{X}^{Y}N \rightarrow _{B}^{A}L + 2\beta \]
Here, \(N\) decays into element \(L\) and emits 2 beta particles. Each beta particle (β) is an electron and does not affect the mass number but increases the atomic number by 1 for each emitted beta particle.

### Step 4: Determine the mass and atomic numbers after the beta decay
- The mass number \(A\) of element \(L\) remains the same as that of \(N\), which is 230.
- The atomic number \(B\) of element \(L\) can be calculated as:
\[ B = 88 + 2 = 90 \]

Thus, the second reaction can be rewritten as:
\[ _{88}^{230}N \rightarrow _{90}^{230}L + 2\beta \]

### Step 5: Calculate the number of neutrons in element \(L\)
To find the number of neutrons in element \(L\), we use the formula:
\[ \text{Number of neutrons} = \text{Mass number} - \text{Atomic number} \]
For element \(L\):
\[ \text{Number of neutrons} = 230 - 90 = 140 \]

### Final Answer
The number of neutrons in element \(L\) is **140**.

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