In Bohr model of hydrogen atom , the electron revolves around the nucleus in a circular orbit of radius `5.1 xx 10^(-11)m` at a frequency of `6.8 xx 10^(15)` revolutions per second. Find the equivalent current at may point on the orbit of the electron

Explanation

To find the equivalent current at any point on the orbit of the electron in a hydrogen atom according to the Bohr model, we can follow these steps:

### Step 1: Understand the Concept of Current
Current (I) is defined as the amount of charge (Q) passing through a point in a circuit per unit time (t). Mathematically, it can be expressed as:
\[ I = \frac{Q}{t} \]

### Step 2: Determine the Charge of the Electron
The charge of an electron (e) is approximately:
\[ e = 1.6 \times 10^{-19} \text{ C} \]

### Step 3: Find the Time Period of Revolution
We are given the frequency (f) of the electron's revolution:
\[ f = 6.8 \times 10^{15} \text{ revolutions per second} \]

The time period (T) is the reciprocal of frequency:
\[ T = \frac{1}{f} = \frac{1}{6.8 \times 10^{15}} \]

### Step 4: Calculate the Time Period
Calculating the time period:
\[ T = \frac{1}{6.8 \times 10^{15}} \approx 1.47 \times 10^{-16} \text{ seconds} \]

### Step 5: Calculate the Equivalent Current
Now, we can substitute the charge and time period into the current formula:
\[ I = \frac{Q}{T} = \frac{e}{T} = \frac{1.6 \times 10^{-19}}{1.47 \times 10^{-16}} \]

### Step 6: Perform the Calculation
Calculating the current:
\[ I \approx \frac{1.6 \times 10^{-19}}{1.47 \times 10^{-16}} \approx 1.088 \times 10^{-3} \text{ A} \]

### Step 7: Convert to Milliamperes
To express the current in milliamperes (mA):
\[ I \approx 1.088 \text{ mA} \]

### Final Answer
The equivalent current at any point on the orbit of the electron is approximately:
\[ I \approx 1.088 \text{ mA} \]

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