A p-type semiconductor is made from a silicon specimen by doping on an average one indium atom per `5xx10^(7)` silicon atoms .If the number density of atoms in the silicon specimen is `5xx10^(26 ) atoms/m^(3)`, then the number of acceptor atoms in silicon per cubic centimetre will be

Options

A. `2.5xx10^(30)`
B. `1.0xx10^(13)`
C. `1.0xx10^(15)`
D. `2.5xx10^(36)`

Answer

To solve the problem of finding the number of acceptor atoms in a p-type semiconductor made from silicon, we can follow these steps:

### Step 1: Understand the given data
We are given:
- The doping ratio: 1 indium atom per \(5 \times 10^7\) silicon atoms.
- The number density of silicon atoms: \(5 \times 10^{26}\) atoms/m³.

### Step 2: Calculate the number of indium atoms per silicon atom
From the doping ratio, we can find the number of indium atoms per silicon atom:
\[ \text{Indium atoms per silicon atom} = \frac{1}{5 \times 10^7} \]

### Step 3: Calculate the total number of silicon atoms in 1 m³
The total number of silicon atoms in 1 m³ is given as:
\[ N_{\text{Si}} = 5 \times 10^{26} \text{ atoms/m}^3 \]

### Step 4: Calculate the total number of indium atoms in 1 m³
Using the ratio from Step 2, we can calculate the total number of indium atoms in 1 m³:
\[ N_{\text{In}} = N_{\text{Si}} \times \frac{1}{5 \times 10^7} = 5 \times 10^{26} \times \frac{1}{5 \times 10^7} \]
\[ N_{\text{In}} = \frac{5 \times 10^{26}}{5 \times 10^7} = 10^{19} \text{ indium atoms/m}^3 \]

### Step 5: Convert the number density from m³ to cm³
Since we need the number of acceptor atoms per cubic centimeter, we convert the density from m³ to cm³:
\[ 1 \text{ m}^3 = 10^6 \text{ cm}^3 \]
Thus, the number of indium atoms per cm³ is:
\[ N_{\text{In/cm}^3} = \frac{10^{19} \text{ indium atoms/m}^3}{10^6 \text{ cm}^3/m^3} = 10^{19 - 6} = 10^{13} \text{ indium atoms/cm}^3 \]

### Final Answer
The number of acceptor atoms in silicon per cubic centimeter is:
\[ \boxed{10^{13} \text{ atoms/cm}^3} \]