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.