A P-type sillicon semiconductor is made by adding one atom of indium per `5xx10^(7)` atoms of sillicon is `25xx10^(28) "atom"//m^(3)`. Point the number of acceptor atoms in per cubic cm. of sillicon

Options

A. `2xx10^(30) "atom"//cm^(3)`
B. `5xx10^(15) "atom"//cm^(3)`
C. `1xx10^(15) "atom"//cm^(3)`
D. `2.5xx10^(36) "atom"//cm^(3)`

Answer

To solve the problem of finding the number of acceptor atoms (indium) per cubic centimeter in a P-type silicon semiconductor, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- We have 1 atom of indium for every \(5 \times 10^7\) atoms of silicon.
- The concentration of silicon atoms is \(25 \times 10^{28}\) atoms/m³.

2. **Calculate the Number of Indium Atoms**:
- We can set up a ratio based on the given information. If there are \(5 \times 10^7\) silicon atoms, there is 1 indium atom.
- Therefore, the number of indium atoms (\(N_{In}\)) in \(25 \times 10^{28}\) silicon atoms can be calculated as follows:
\[ N_{In} = \frac{1 \text{ indium atom}}{5 \times 10^7 \text{ silicon atoms}} \times 25 \times 10^{28} \text{ silicon atoms} \]

3. **Perform the Calculation**:
- Plugging in the numbers:
\[ N_{In} = \frac{25 \times 10^{28}}{5 \times 10^7} \]
- Simplifying this gives:
\[ N_{In} = 5 \times 10^{21} \text{ indium atoms/m}^3 \]

4. **Convert to Atoms per Cubic Centimeter**:
- Since we need the answer in atoms per cubic centimeter, we convert from cubic meters to cubic centimeters.
- There are \(100^3 = 10^6\) cubic centimeters in a cubic meter.
- Therefore, we divide by \(10^6\):
\[ N_{In} = \frac{5 \times 10^{21}}{10^6} = 5 \times 10^{15} \text{ indium atoms/cm}^3 \]

5. **Final Answer**:
- The number of acceptor atoms (indium) per cubic centimeter in silicon is:
\[ \boxed{5 \times 10^{15} \text{ atoms/cm}^3} \]