The average distance of electron from the nucleus in an atom is of the order of

Options

A. 1 cm
B. `10^(-13) cm`
C. `10^(-8) cm`
D. 1 mm

Answer

To find the average distance of an electron from the nucleus in an atom, we can use the formula for the radius of an electron's orbit in a hydrogen atom. Here’s a step-by-step solution:

### Step 1: Understand the Formula
The average distance (or radius) of an electron from the nucleus in a hydrogen atom can be calculated using the formula:
\[ R = \frac{0.529 \, \text{Å} \cdot n^2}{Z} \]
where:
- \( R \) is the radius,
- \( n \) is the principal quantum number (energy level),
- \( Z \) is the atomic number.

### Step 2: Identify Values for Hydrogen
For hydrogen:
- The atomic number \( Z = 1 \).
- The principal quantum number for the ground state \( n = 1 \).

### Step 3: Substitute the Values
Substituting the values into the formula:
\[ R = \frac{0.529 \, \text{Å} \cdot (1)^2}{1} \]
\[ R = 0.529 \, \text{Å} \]

### Step 4: Convert Angstroms to Meters
1 Ångström (Å) is equal to \( 10^{-10} \) meters. Therefore:
\[ R = 0.529 \, \text{Å} = 0.529 \times 10^{-10} \, \text{m} \]

### Step 5: Convert to Centimeters
To convert meters to centimeters, we know that:
1 meter = 100 centimeters. Thus:
\[ R = 0.529 \times 10^{-10} \, \text{m} = 0.529 \times 10^{-8} \, \text{cm} \]

### Step 6: Express in Scientific Notation
We can express this in scientific notation:
\[ R \approx 5.29 \times 10^{-9} \, \text{cm} \]

### Conclusion
The average distance of the electron from the nucleus in a hydrogen atom is of the order of \( 10^{-8} \) cm.

### Final Answer
The average distance of the electron from the nucleus in an atom is of the order of \( 10^{-8} \) cm.

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