In hydrogen atom, the electron makes `6.6 xx 10^(15)` revolutions per second around the nucleus in an orbit of radius `0.5 xx 10^(-10)m`. It is equivalent to a current nearly

Options

A. `1A`
B. `1mA`
C. `1 muA`
D. `1.6 xx 10^(-19)A`

Answer

To find the equivalent current due to the electron revolving around the nucleus in a hydrogen atom, we can follow these steps:

### Step 1: Understand the relationship between current, charge, and time
Current (I) is defined as the charge (Q) passing through a point in a circuit per unit time (T). Mathematically, this is expressed as:
\[ I = \frac{Q}{T} \]

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

### Step 3: Calculate the time period (T) of one revolution
The time period (T) can be calculated using the frequency (f), which is given as \( 6.6 \times 10^{15} \) revolutions per second. The time period is the reciprocal of frequency:
\[ T = \frac{1}{f} \]
Substituting the value of frequency:
\[ T = \frac{1}{6.6 \times 10^{15}} \text{ seconds} \]

### Step 4: Calculate the current (I)
Now, substituting the values of Q and T into the current formula:
\[ I = \frac{Q}{T} = Q \times f \]
Substituting the values:
\[ I = (1.6 \times 10^{-19} \text{ C}) \times (6.6 \times 10^{15} \text{ Hz}) \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ I = 1.6 \times 6.6 \times 10^{-19 + 15} \]
\[ I = 10.56 \times 10^{-4} \text{ A} \]
\[ I \approx 1.056 \times 10^{-3} \text{ A} \]
\[ I \approx 1.056 \text{ mA} \]

### Conclusion
The equivalent current due to the electron revolving around the nucleus in a hydrogen atom is approximately:
\[ I \approx 1.056 \text{ mA} \]