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)`
B. `2.5xx10^(35)`
C. `1.0xx10^(13)`
D. `1.0xx10^(15)`

Answer

To solve the problem, we need to determine the number of acceptor atoms (helium atoms) in a silicon specimen per cubic centimeter. Here’s a step-by-step breakdown of the solution:

### Step 1: Understand the Given Data
- The number density of silicon atoms is given as \( n_{Si} = 5 \times 10^{28} \, \text{atoms/m}^3 \).
- The doping ratio is 1 helium atom for every \( 5 \times 10^7 \) silicon atoms.

### Step 2: Convert the Number Density from \( \text{atoms/m}^3 \) to \( \text{atoms/cm}^3 \)
To convert from \( \text{atoms/m}^3 \) to \( \text{atoms/cm}^3 \), we use the conversion factor \( 1 \, \text{m}^3 = 10^6 \, \text{cm}^3 \).

\[ n_{Si} = 5 \times 10^{28} \, \text{atoms/m}^3 \times \frac{1 \, \text{m}^3}{10^6 \, \text{cm}^3} = 5 \times 10^{28} \times 10^{-6} \, \text{atoms/cm}^3 = 5 \times 10^{22} \, \text{atoms/cm}^3 \]

### Step 3: Calculate the Number of Acceptor Atoms
Given that there is 1 helium atom for every \( 5 \times 10^7 \) silicon atoms, we can find the number of helium atoms (acceptor atoms) per cubic centimeter using the formula:

\[ n_{He} = \frac{n_{Si}}{5 \times 10^7} \]

Substituting the value of \( n_{Si} \):

\[ n_{He} = \frac{5 \times 10^{22}}{5 \times 10^7} = \frac{5}{5} \times 10^{22 - 7} = 1 \times 10^{15} \, \text{atoms/cm}^3 \]

### Step 4: Conclusion
The number of acceptor atoms in silicon per cubic centimeter is:

\[ \boxed{1 \times 10^{15} \, \text{atoms/cm}^3} \]