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In the Bohr model, the electron of a hydrogen atom moves in a circular orbit of radius 5.3*10^{-11} m with a speed of 2.2*10^6 m/s. Determine its frequency f and the current I in the orbit. 

  • Option 1)

    1.06 mA

  • Option 2)

    2.06 mA

  • Option 3)

    0.06 mA

  • Option 4)

    3.06 mA

 

Answers (1)

best_answer

As we learnt

 

Current due to rotatory motion of charge -

 

i=\frac{q}{t}=\frac{qv}{2\pi r}=\frac{qw}{2\pi}

- wherein

 

 

 

f = \frac{\nu }{{2\pi r}} = \frac{{2.2 \times {{10}^6}\,m/s}}{{2\pi (5.3 \times {{10}^{ - 11}}m)}} = 6.6 ´ 1015 rev/s

                              Each time the electron goes around the orbit, it carries a charge e around the loop. The charge passing a point on the loop each second is

                              current = I = ef = (1.6 ´ 10–19C) (6.6 ´ 1015s–1) = 1.06 mA.

                                 Note that the current flows in the opposite direction to the electron, which is negatively charged.


Option 1)

1.06 mA

Option 2)

2.06 mA

Option 3)

0.06 mA

Option 4)

3.06 mA

Posted by

Plabita

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