Question

In the Bohr model of the hydrogen atom, an electron in the 7th excited state moves at a speed of 4.47 104 m/s in a circular path having a radius of 2.59 10-9 m. What is the effective current associated with this orbiting electron

Answer 1

Answer:

I = 4.38 x 10⁻⁷ A

Explanation:

Given,

speed = 4.47 x 10⁴ m/s

radius of the circular path, r = 2.59 x 10⁻⁹ m

effective current = ?

The current represented by the orbiting electron is equal to

$I = q \times f$

f is the frequency

q is charge of electron

we know,

$f = \dfrac{v}{2\pi r}$

$f = \dfrac{4.47\times 10^{4}}{2\pi\times 2.59\times 10^{-9}}$

f = 2.74 x 10¹² Hz

now,

$I = 1.6 \times 10^{-19}\times 2.74\times 10^{12}$

I = 4.38 x 10⁻⁷ A

Hence, the effective current associated with the orbiting electron is equal to I = 4.38 x 10⁻⁷ A

Answer 2

Answer:

4.4 x 10^-7 A

Explanation:

charge on an electron, q = 1.6 x 10^-19 C

velocity, v = 4.47 x 10^4 m/s

radius, r = 2.59 x 10^-9 m

Let the effective current is i.

According to the definition of current, the rate of flow of charge through the conductor is called current.

i = q / T

where, T is the time period of rotation.

$T = \frac{2\pi r }{v}$

$T = \frac{2\times 3.14\times 2.59\times 10^{-9} }{4.47\times 10^{4}}$

T = 3.64 x 10^-13 s

So, current

$i=\frac{1.6\times 10^{-19}}{3.64\times 10^{-13}}$

i = 4.4 x 10^-7 A