Question regarding Atomic Structure (orbits)

[Sanosuke Sagara]

I have my doubt,solution and question in the attachment that followed.Thanks for anybody that spend some time on this question.

 

[jtbell]

It's only a coincidence that you got the right number for part (a). The fact that using the same procedure for part (b) gives the wrong answer, is a good indicator that you are using the wrong procedure.

Your problem is that you are calculating 1 / \lambda which is not a number of revolutions. It's simply the reciprocal of the wavelength, with units of 1/meters. The answer you need doesn't have any units; it's just a "counting" number.

I suggest that you look in your textbook for equations related to the speed v of the electron in an orbit with quantum number n, and the radius r of that orbit. If you know those quantities, you can calculate the time the electron takes for one orbit (the period, T), and from that, the number of orbits it makes in 10^{-8} seconds.

 

[Dr.Brain]

Ok first of all, calculate the wavelength emitted , in the same way you have calculated in your doc-attachment.then calculate the velocity of the electron in n=2 , i hope you can do that.
then v= (frequency) (wavelength)
calculate frequency with the above formula , this will be give you cycles /sec

Now you want cycles in 10^-8 seconds , use unitary method.I am getting the correct answer.

 

[Sanosuke Sagara]

Yes your both are right and I admit that I just have the 'luck' getting the first answer right and not the second.Thanks for your both detail explanation,jtbell and Dr.Brain,I really appreciate it.