Question

In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton, where the radius of the orbit is approximately 0.550 ✕ 10-10 m. (The actual value is 0.529 ✕ 10-10 m.)

(a) Find the electric force exerted on each particle, based on the approximate (not actual) radius given.
(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?

Answer 1

Step-by-step explanation:

It is given that,

Radius of orbit,
`r=0.55* 10^(-10)\ m`

Charge on electron,
`q=1.6* 10^(-19)\ C`

(a) The electric force exerted on each particle is given by :

`F=k(q^2)/(r^2)`

`F=9* 10^9* ((1.6* 10^(-19))^2)/((0.55* 10^(-10))^2)`

`F=7.61* 10^(-8)\ N`

(b) If this force causes the centripetal acceleration of the electron, then we need to find the speed of the electron. Let v is the speed,

So,
`F=(mv^2)/(r)`

`v=\sqrt{(Fr)/(m)}`

`v=\sqrt{(7.61* 10^(-8)* 0.55* 10^(-10))/(9.1* 10^(-31))}`

v = 2144632.96 m/s

or

`v=2.14* 10^6\ m/s`

Hence, this is the required solution.