Electric Force Help?

Question

Hey guys... i'm having trouble with two questions...can anyone help? Thanks in advance!

1. In the Bohr theory of the hydrogen atom, an electron moves in a circular orbit about a proton. The radius of the orbit is 0.53x10^-10m. If this force causes the centripetal acceleration of the electron, what is the speed of the electron?

2. A positively charged beat having a mass of 1.00g falls from rest in a vacuum from a heigh of 5.00m in a uniform vertical electric field with a magnitude of 1.00x10^4 N/C. The bead hits the ground at a speed of 21.0 m/s. Determine the charge of the bead.

Answer 1

Ok. I understand the firs question :

1. If the force causes the centripetal acceleration, then the force between the electron and the proton is equal to the centripetal force

So :

the electrical force : K*q1*q2 / r^2

where q1 = q2 = 1.6*10^-19 C

r = radius

k = constant = 9*10^9

centripetal force = m*v^2/ r

v = speed of the electron

m = mass of the electron = 9.1*10^-31 kg

then :

9.1*10^-31*v^2 /0.53*10^-10 = 9*10^9*(1.6*10^-19)^2 / 0.53*10^-20

be careful when you obtain the speed, the answer is bellow

v = 2.18*10^6 m/s

2. the beat falls, and gains speed because of the electrical field, so we can calculate the acceleration of the beat, how ?

like this :

Eq = ma

where m = 1*10^-3 kg

E = 1*10^4 N/C

10^4*q = 10^-3*a

the initial speed = 0

final speed = 21

height = 21

then using the formula : Vf^2 = Vo^2 +2ae

21^2 = 2*a*5

acceleration = 44.1 m/s^2

now, we use the acceleration in :

Eq = ma

10^4*q = 10^-3*44.1

q = 44.1*10^-7 C

or q = 4.41*10-6 C >>> 4.41 micro Coulomb