Electron orbital speed in hydrogen atom model

[discostu]

I'm trying to solve this problem correctly, but my calculations yield a different result than the correct answer according to my professor.

In a semi-classical model of the neutral hydrogen atom, an electron of charge -e and of mass 9.1*10^-31 undergoes uniform circular motion around the much more massive proton with charge +e. The radius of the electron's orbit is 5.3*10^-11 m. The speed of the electron in its orbit is ____ m/s.

(Force Elec) = (m * a)

=> e^2/(4*pi*E0*radius^2) = mass*velocity^2/radius

=>velocity = (e^2/(4*pi*E0*radius*mass))^(1/2)

where 1/(4*pi*E0) = 8.99*10^9 Nm^2/C^2 and e = 1.602*10^-19

When I solve the equation I get ((1.6*10^-19)^2/(8.99*10^9 * 5.3*10^-11 * 9.1*10^-31))^(1/2) = 2.43*10^-4 m/s, however they say the correct answer is 2.2*10^6 m/s

Maybe I'm doing something wrong? I would hope the prof did everything correctly.

 

[sridhar_n]

...

What you should do is equate the electric potential energy to the kinetic energy of the electron...Thats all that you need to do and lo behold you have the answer.

i.e.


$$(e^2)/(4\Pi \epsilon_{0}r) = 1/2*(mv^2 )$$

From the above equation you can find the velocity...


Sridhar

 

[discostu]

Originally posted by sridhar_n
What you should do is equate the electric potential energy to the kinetic energy of the electron...Thats all that you need to do and lo behold you have the answer.

i.e.


$$(e^2)/(4\Pi \epsilon_{0}r) = 1/2*(mv^2 )$$

From the above equation you can find the velocity...


Sridhar

This is the equation I was using. The mistake I made was putting the value for $$1/(4\Pi \epsilon_{0}) = 8.99*10^9$$ in the denominator of my calculation, instead of the numerator where it should go.

 

[sridhar_n]

...

As u said you must substitute $$1/4\Pi\epsilon_{0} = 8.99 * 10^9$$ in the numerator.

i.e.

$$8.99*10^9 * (e^{2})/r = 1/2 * mv^2$$


Sridhar