The total electric flux emanating from a closed surface enclosing an alpha particale (e = electronic chage) is

Options

A. `(2e)/(epsi_(0))`
B. `(e)/(epsi_(0))`
C. `e epsi_(0)`
D. `(epsi_(0)e)/(4)`

Answer

To solve the problem of finding the total electric flux emanating from a closed surface enclosing an alpha particle, we can follow these steps:

### Step 1: Understand the charge of the alpha particle
An alpha particle consists of 2 protons and 2 neutrons. Since neutrons do not carry any charge, we only consider the charge from the protons. Each proton has a charge of \( e \), where \( e \) is the elementary charge. Therefore, the total charge \( Q \) of an alpha particle is:
\[ Q = 2e \]

### Step 2: Apply Gauss's Law
Gauss's Law states that the total electric flux \( \Phi \) through a closed surface is equal to the charge enclosed \( Q \) divided by the permittivity of free space \( \epsilon_0 \):
\[ \Phi = \frac{Q}{\epsilon_0} \]

### Step 3: Substitute the charge into Gauss's Law
Now, substituting the charge of the alpha particle into Gauss's Law:
\[ \Phi = \frac{2e}{\epsilon_0} \]

### Step 4: Conclusion
Thus, the total electric flux emanating from the closed surface enclosing the alpha particle is:
\[ \Phi = \frac{2e}{\epsilon_0} \]

### Final Answer
The total electric flux emanating from a closed surface enclosing an alpha particle is \( \frac{2e}{\epsilon_0} \).