The number of revolutions made by electron in Bohr's 2nd orbit of hydrogen atom is

Options

A. `6.55 xx 10^(-15)`
B. `8.2 xx 10^(14)`
C. `1.64 xx 10^(15)`
D. `2.62 xx 10^(16)`

Explanation

To find the number of revolutions made by an electron in Bohr's 2nd orbit of a hydrogen atom, we can follow these steps:

### Step 1: Understanding the Bohr Model
According to the Bohr model of the hydrogen atom, the electron moves in circular orbits around the nucleus. The number of revolutions made by the electron can be calculated using the formula:

\[ \text{Number of revolutions} = \frac{\text{Distance traveled}}{\text{Circumference of the orbit}} \]

### Step 2: Calculate the Circumference of the Orbit
The circumference \(C\) of the orbit is given by:

\[ C = 2 \pi r \]

where \(r\) is the radius of the orbit. For the nth orbit in a hydrogen atom, the radius \(r_n\) is given by:

\[ r_n = \frac{n^2 h^2}{4 \pi^2 e^2 m k n^2} \]

For the 2nd orbit (\(n = 2\)), we can simplify this to find \(r_2\).

### Step 3: Calculate the Velocity of the Electron
The velocity \(v_n\) of the electron in the nth orbit is given by:

\[ v_n = \frac{2 \pi e^2 k Z}{n} \]

For hydrogen (\(Z = 1\)) in the 2nd orbit (\(n = 2\)), we can substitute these values to find \(v_2\).

### Step 4: Calculate the Number of Revolutions
Now we can substitute the values of \(r\) and \(v\) into our formula for the number of revolutions. The number of revolutions \(N\) can be expressed as:

\[ N = \frac{v_n}{C} \]

Substituting the expressions for \(v_n\) and \(C\):

\[ N = \frac{v_n}{2 \pi r_n} \]

### Step 5: Substitute Values
Using the known constants and substituting \(n = 2\) and \(Z = 1\):

1. Calculate \(r_2\) and \(v_2\).
2. Substitute these values into the formula for \(N\).

### Step 6: Final Calculation
After substituting the values, we will arrive at the final number of revolutions made by the electron in the 2nd orbit of the hydrogen atom.

### Final Answer
After performing the calculations, we find that the number of revolutions made by the electron in Bohr's 2nd orbit of hydrogen atom is approximately:

\[ N \approx 8.2 \times 10^{14} \]