In the Bohr model of the hydrogen atom, an electron in the 8th excited state moves at a speed of 3.42 104 m/s in a circular path having a radius of 3.39 10-9 m. What is the effective current associated with this orbiting electron

I=1.6x10-19A

Explanation:

Given Info: Electron in its lowest energy

state moves with the velocity

2.19x 10" m. s in a circular orbit of

radius 5.29 x 10" m, Electron in its lowest

energy state moves with the velocity

2.19 x 10 m-s" in a circular orbit of

radius 5.29 x 10- m.

Explanation:

Formula to calculate the time period of

electron is,

T:

2TT

21

Tis the time period of electron,

ris the radius of circular orbit,

vis the velocity of electron,

Substitute 3.14 for T, 5.29 x 10- m for r

and 2.19x 10 m s for v in the above

equation to find T.

T23.14) (5.29 x 10-1 m)

T-

2.19x10 ms

= 1

Let the current be:

I

=

d

Q

d

t

Where Q is the charge.

If rate of flow of charge is not constant then the current at any instant is given by the differential limit: I = dQ/dt.

If a charge Q flows through the circuit for time t, then

 I = Q/t.

Charge of hydrogen atom q = 1.6x10–19C

T = 1

Therefore,

I = 1.6 x 10-19C/1

I=1.6x10-19A