A silicon specimen is made into a p type semiconductor

on an average one indium atom per 5 * 10^7 silicon atoms

if the number density in the silicon specimen is 5 * 10^28 atoms/m^3 then the nos of acceptor atoms in silicon per cubic m^3 will be

Ans 10^15

Please give detai;led solution rates as usual assured

To determine the number of acceptor atoms in a silicon specimen that has been doped to create a p-type semiconductor, we can follow a straightforward calculation based on the information provided. Let's break it down step by step.

Understanding the Problem

We know that the silicon specimen has a certain number density of silicon atoms and that indium atoms are introduced as acceptor atoms. The key points from your question are:

• Density of silicon atoms: \(5 \times 10^{28}\) atoms/m³
• Ratio of indium atoms to silicon atoms: 1 indium atom per \(5 \times 10^7\) silicon atoms

Calculating the Number of Acceptor Atoms

To find the number of acceptor atoms (indium) per cubic meter, we can use the ratio of indium to silicon atoms. The formula to calculate the number of indium atoms is as follows:

Number of Indium Atoms (N_indium) = (Number Density of Silicon Atoms) / (Ratio of Silicon to Indium)

Substituting the values we have:

N_indium = (5 × 10²⁸ atoms/m³) / (1 indium atom / (5 × 10⁷ silicon atoms))

Performing the Calculation

Now, let's simplify the calculation:

N_indium = (5 × 10²⁸) × (5 × 10⁷)

When we multiply these two numbers, we get:

N_indium = 25 × 10³⁵ atoms/m³

However, since we are looking for the number of acceptor atoms per cubic meter, we need to adjust this result. The ratio indicates that for every \(5 \times 10^7\) silicon atoms, there is 1 indium atom. Therefore, we need to divide the total number of silicon atoms by the ratio:

N_indium = (5 × 10²⁸) / (5 × 10⁷)

Now, simplifying this gives:

N_indium = 10²¹ atoms/m³

Final Result

Thus, the number of acceptor atoms (indium) in the silicon specimen per cubic meter is:

N_indium = 10²¹ atoms/m³

It seems there was a misunderstanding in your initial assertion that the answer is \(10^{15}\). Based on the calculations, the correct number of acceptor atoms in the silicon per cubic meter is \(10^{21}\). If you have any further questions or need clarification on any of the steps, feel free to ask!