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In a hydrogen atom the electron makes about 0.6*10^16 revolutions per second around the nucleus.Determine the average current at any point on the orbit of the electron?
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In a hydrogen atom the electron makes about 0.6*10^16 revolutions per ...
Calculation of Average Current in a Hydrogen Atom

When an electron revolves around the nucleus, it results in a current. The average current in a hydrogen atom can be calculated using the given formula:


Average Current = (charge of the electron * number of revolutions per second) / (time period of one revolution)


Charge of the Electron
The charge of an electron is -1.6 x 10^-19 coulombs.


Number of Revolutions per Second
Given, the electron in a hydrogen atom makes 0.6 x 10^16 revolutions per second around the nucleus.


Time Period of One Revolution
The time period of one revolution can be calculated using the formula:


Time period = (2πr) / (velocity of the electron)


Where r is the radius of the orbit and velocity of the electron is given by:


Velocity of the electron = (charge of the electron * radius of the orbit) / (mass of the electron * ε0 * h)


Where ε0 is the permittivity of free space and h is Planck's constant.


The radius of the first orbit in a hydrogen atom is given by:


r = (ε0 * h^2) / (π * m * e^2)


Where m is the mass of the electron and e is the charge of the electron.


Substituting the Values

Using the above formulas and substituting the values, we get:


Radius of the orbit (r) = 5.29 x 10^-11 m


Velocity of the electron = 2.19 x 10^6 m/s


Time period of one revolution = 2.42 x 10^-16 s


Average Current = (-1.6 x 10^-19 * 0.6 x 10^16) / (2.42 x 10^-16) = -3.98 x 10^-3 A


Interpretation

The negative sign in the answer indicates that the current flows in the opposite direction to the motion of the electron. The magnitude of the current is very small due to the small size of the atom. However, this current is responsible for the stability of the atom and the emission/absorption of electromagnetic radiation during transitions between different energy levels.
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In a hydrogen atom the electron makes about 0.6*10^16 revolutions per second around the nucleus.Determine the average current at any point on the orbit of the electron?
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