In hydrogen atom an orbit has a diameter of about `16.92 Å`, what is the maximum number of electrons that can be accommodated in that orbit.

Options

A. 8
B. 32
C. 50
D. 72

Explanation

To determine the maximum number of electrons that can be accommodated in an orbit with a diameter of about `16.92 Å`, we can follow these steps:

### Step 1: Calculate the radius of the orbit
The diameter of the orbit is given as `16.92 Å`. To find the radius, we divide the diameter by 2.

\[ \text{Radius} = \frac{\text{Diameter}}{2} = \frac{16.92 \, \text{Å}}{2} = 8.46 \, \text{Å} \]

### Step 2: Convert the radius to meters
Since the standard unit for calculations in physics is meters, we convert the radius from angstroms to meters.

\[ 1 \, \text{Å} = 1 \times 10^{-10} \, \text{m} \]
\[ \text{Radius} = 8.46 \, \text{Å} = 8.46 \times 10^{-10} \, \text{m} \]

### Step 3: Use the formula for the maximum number of electrons in an orbit
The maximum number of electrons that can be accommodated in a given orbit is determined by the formula:

\[ \text{Maximum number of electrons} = 2n^2 \]

where \( n \) is the principal quantum number.

### Step 4: Determine the principal quantum number \( n \)
The principal quantum number \( n \) can be estimated from the radius of the orbit. For hydrogen, the radius of the \( n \)-th orbit is given by:

\[ r_n = n^2 \times a_0 \]

where \( a_0 \) (Bohr radius) is approximately \( 5.29 \times 10^{-11} \, \text{m} \).

Rearranging the formula to find \( n \):

\[ n^2 = \frac{r_n}{a_0} \]

Substituting the values:

\[ n^2 = \frac{8.46 \times 10^{-10} \, \text{m}}{5.29 \times 10^{-11} \, \text{m}} \approx 16 \]

Taking the square root:

\[ n \approx 4 \]

### Step 5: Calculate the maximum number of electrons
Now that we have \( n \):

\[ \text{Maximum number of electrons} = 2n^2 = 2 \times 4^2 = 2 \times 16 = 32 \]

### Final Answer
The maximum number of electrons that can be accommodated in the orbit is **32**.

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