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 0.522 ✕ 10-10 m. (The actual value is 0.529 ✕ 10-10 m.) (a) Find the magnitude of the electric force exerted on each particle.

(b) If this force causes the centripetal acceleration of the electron, what is the speed of the electron?

Answer 1

a)
`8.5* 10^(-8)` N

b)
`2.2* 10^(6)` m/s

Step-by-step explanation:

a)

`r` = radius of the orbit = 0.522 x 10⁻¹⁰ m

`q` = magnitude of charge on each proton and electron = 1.6 x 10⁻¹⁹ C

Using coulomb's law , magnitude of electric force on the particle is given as

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

`F = ((9* 10^(9))(1.6* 10^(-19))^(2))/((0.522* 10^(-10))^(2))`

`F = 8.5* 10^(-8)` N

b)

`m` = mass of electron = 9.1 x 10⁻³¹ kg

`v` = speed of electron = ?

Centripetal force is being provided by the electric force, hence

Centripetal force = electric force

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

`((9.1* 10^(-31))v^(2))/(0.522* 10^(-10)) = 8.5* 10^(-8)`

`v = 2.2* 10^(6)` m/s