The electric current I created by the electron in the ground state of H atom bohr model in terms of bohr radius `(a_0)` and velocity of electron in first orbit `v_0` is

Options

A. `(ev_0)/(2pia_0)`
B. `(2pia)/(ev_0)`
C. `(2pia)/(v_0)`
D. `(v_0)/(2pia)`

Explanation

To find the electric current \( I \) created by the electron in the ground state of a hydrogen atom according to the Bohr model, we can follow these steps:

### Step 1: Understand the definition of electric current
Electric current \( I \) is defined as the rate of flow of charge. Mathematically, it can be expressed as:
\[ I = \frac{Q}{T} \]
where \( Q \) is the charge and \( T \) is the time period for one complete revolution.

### Step 2: Identify the charge of the electron
The charge of an electron \( e \) is approximately \( 1.6 \times 10^{-19} \) coulombs.

### Step 3: Determine the time period \( T \) for one complete revolution
The electron revolves in a circular orbit of radius \( a_0 \) (the Bohr radius). The circumference of this orbit is given by:
\[ \text{Circumference} = 2 \pi a_0 \]
The time period \( T \) can be calculated using the formula:
\[ T = \frac{\text{Circumference}}{\text{Velocity}} = \frac{2 \pi a_0}{v_0} \]

### Step 4: Substitute \( Q \) and \( T \) into the current formula
Now, substituting the values of \( Q \) and \( T \) into the current formula:
\[ I = \frac{Q}{T} = \frac{e}{\frac{2 \pi a_0}{v_0}} = \frac{e v_0}{2 \pi a_0} \]

### Final Expression
Thus, the electric current \( I \) created by the electron in the ground state of the hydrogen atom in terms of the Bohr radius \( a_0 \) and the velocity of the electron \( v_0 \) is:
\[ I = \frac{e v_0}{2 \pi a_0} \]