A silicon specimen is made into a `P`-type semiconductor by dopping, on an average, one helium atoms per `5xx10^(7)` silicon atoms. If the number density of atoms in the silicon specimen is `5xx10^(28) at om//m^(3)` then the number of acceptor atoms in silicon per cubic centimeter will be

Options

A. `2.5xx10^(30) at oms//cm^(3)`
B. `1.0xx10^(13) at oms//cm^(3)`
C. `1.0xx10^(15) at oms//cm^(3)`
D. `2.5xx10^(36) at oms//cm^(3)`

Explanation

To find the number of acceptor atoms in silicon per cubic centimeter, we can follow these steps:

### Step 1: Understand the given data
- The average number of helium atoms (which act as acceptors) per silicon atom is given as \( 1 \text{ He atom} / (5 \times 10^7 \text{ Si atoms}) \).
- The number density of silicon atoms is given as \( 5 \times 10^{28} \text{ atoms/m}^3 \).

### Step 2: Calculate the number density of acceptor atoms
To find the number density of acceptor atoms, we can use the ratio of helium atoms to silicon atoms.

\[ \text{Number density of acceptor atoms} = \frac{1 \text{ He atom}}{5 \times 10^7 \text{ Si atoms}} \times \text{Number density of Si atoms} \]

Substituting the value of the number density of silicon atoms:

\[ \text{Number density of acceptor atoms} = \frac{1}{5 \times 10^7} \times 5 \times 10^{28} \]

### Step 3: Simplify the calculation
Now, we can simplify the expression:

\[ \text{Number density of acceptor atoms} = \frac{5 \times 10^{28}}{5 \times 10^7} = 10^{21} \text{ atoms/m}^3 \]

### Step 4: Convert to cubic centimeters
Since we need the number of acceptor atoms per cubic centimeter, we need to convert from cubic meters to cubic centimeters.

1 cubic meter = \( 10^6 \) cubic centimeters, so:

\[ \text{Number density of acceptor atoms in } \text{cm}^3 = \frac{10^{21} \text{ atoms/m}^3}{10^6 \text{ cm}^3/\text{m}^3} = 10^{15} \text{ atoms/cm}^3 \]

### Final Answer
The number of acceptor atoms in silicon per cubic centimeter is \( 10^{15} \text{ atoms/cm}^3 \).

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