Question

Electron in the hydrogen atom is moving round the nucleus with \(6.0 \times 10^{15}\) cycle per second. What will be the value of current at a point on circular path ?

Hint:

Remember that "cycles per second" is just another way of stating the frequency in Hertz (Hz). The concept of an orbiting charge creating a current is fundamental in understanding the magnetic properties of atoms (orbital magnetic moment).

Answer 1

Step 1: Understanding the Concept:
An electron revolving in a circular orbit constitutes an electric current. The current is defined as the rate of flow of charge. For a revolving electron, the current at any point on the orbit is the total charge that passes that point per unit time.
Step 2: Key Formula or Approach:
The electric current (I) is given by: \[ I = \frac{Q}{t} \] In this case, Q is the charge of the electron (e), and the time taken for one revolution is the time period (T). So, \( I = \frac{e}{T} \).
The frequency (f) is the number of cycles per second, which is the reciprocal of the time period (\( f = 1/T \)). Therefore, the formula can be written as: \[ I = e . f \] Step 3: Detailed Explanation:
We are given:
Frequency of revolution \( f = 6.0 \times 10^{15} \) cycles/second (or Hz).
The charge of an electron \( e = 1.6 \times 10^{-19} \) C.
Now, we can calculate the current using the formula \( I = ef \): \[ I = (1.6 \times 10^{-19} \, \text{C}) \times (6.0 \times 10^{15} \, \text{s}^{-1}) \] \[ I = (1.6 \times 6.0) \times 10^{-19 + 15} \, \text{C/s} \] \[ I = 9.6 \times 10^{-4} \, \text{A} \] This can also be expressed as: \[ I = 0.96 \times 10^{-3} \, \text{A} = 0.96 \, \text{mA} \] Step 4: Final Answer:
The value of the current at a point on the circular path is \( 9.6 \times 10^{-4} \) A or 0.96 mA.