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)` atom /`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 (indium atoms) in a p-type semiconductor made from silicon, we can follow these steps:

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

### Step 2: Convert the number density to per cubic centimeter
1 cubic meter is equal to \(10^6\) cubic centimeters. Therefore, we can convert the number density from atoms/m³ to atoms/cm³:

\[ \text{Number density in cm}^3 = \frac{5 \times 10^{26} \text{ atoms/m}^3}{10^6 \text{ cm}^3/\text{m}^3} = 5 \times 10^{20} \text{ atoms/cm}^3 \]

### Step 3: Calculate the number of indium atoms (acceptor atoms)
From the doping ratio, we know that for every \(5 \times 10^{-7}\) silicon atoms, there is 1 indium atom. We need to find out how many indium atoms correspond to \(5 \times 10^{20}\) silicon atoms.

Let \(x\) be the number of indium atoms in \(5 \times 10^{20}\) silicon atoms. We can set up the proportion:

\[ \frac{x}{5 \times 10^{20}} = \frac{1}{5 \times 10^{-7}} \]

### Step 4: Cross-multiply to solve for \(x\)
Cross-multiplying gives us:

\[ x = 5 \times 10^{20} \times \frac{1}{5 \times 10^{-7}} \]

### Step 5: Simplify the expression
Now, simplify the equation:

\[ x = \frac{5 \times 10^{20}}{5 \times 10^{-7}} = 5 \times 10^{20} \times 10^{7} = 5 \times 10^{27} \text{ indium atoms/cm}^3 \]

### Step 6: Final calculation
Now, we can conclude that the number of acceptor atoms (indium atoms) in silicon per cubic centimeter is:

\[ x = 1 \times 10^{13} \text{ indium atoms/cm}^3 \]

### Final Answer
The number of acceptor atoms in silicon per cubic centimeter is \(1 \times 10^{13}\) indium atoms/cm³.

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