Homework Help: Find frequency

1. Jul 30, 2011

Saitama

1. The problem statement, all variables and given/known data
When an electron makes a transition from (n+1) state to nth state, the frequency of emitted radiations is related to n according to (n>>1):
(a)$v=\frac{2cRZ^2}{n^3}$
(b)$v=\frac{cRZ^2}{n^4}$
(c)$v=\frac{cRZ^2}{n^2}$
(a)$v=\frac{2cRZ^2}{n^2}$

2. Relevant equations
$$\frac{1}{\lambda}=RZ^2(\frac{1}{n_1^2}-\frac{1}{n_2^2})$$

3. The attempt at a solution
Solving the above equation and substituting the values i get:-
$$v=cRZ^2(\frac{1}{n^2}-\frac{1}{(n+1)^2})$$

$$v=cRZ^2(\frac{2n+1}{n^2(n+1)^2})$$

Now i am stuck, what should i do next?

2. Jul 30, 2011

pmsrw3

It's always a good idea when you're having trouble with a math problem to check whether you've used all the information given. You haven't used n>>1.

3. Jul 30, 2011

Saitama

I don't know how should i use n>>1?

4. Jul 30, 2011

pmsrw3

Well, try an example. Substitute in a big n, 100 for instance, and see what you get. Check whether it's closer to a, b, c, or d. Then try to figure out why.

5. Jul 30, 2011

Saitama

That's a lot of calculation if i substitute n=100, and i am not able to solve it.
When i substitute n=100, i get:-
$$v=cRZ^2(\frac{201}{10000(10201)})$$

6. Jul 30, 2011

pmsrw3

There's nothing to solve! Just punch it into your calculator and see what you get. Or use http://www.google.com/landing/searchtips/#calculator". Then do the same for the four choices you're given.

No, that is not a lot of calculation. That's a small amount of easy calculations. You need to get used to calculating things if you're going to be taking science classes.

Last edited by a moderator: Apr 26, 2017
7. Jul 30, 2011

Saitama

Sorry, i can't use a calculator, this question is from my exam paper and in the examination room we were not allowed to use a calculator, so any other way to solve it?

Last edited by a moderator: Apr 26, 2017
8. Jul 30, 2011

pmsrw3

Are you in the exam room now? If so, you shouldn't be asking for help. If not, then you can use a calculator.

9. Jul 30, 2011

Saitama

No, don't talk silly, how can i be in the examination room and post a question?

10. Jul 30, 2011

pmsrw3

So use a calculator.

11. Jul 30, 2011

Saitama

Ok i did it using a calculator, i get my answer to be (a) option.

12. Jul 30, 2011

pmsrw3

Good. Now see if you can figure out why it comes out so close. If it's not obvious, try a few other n's.

13. Jul 30, 2011

Saitama

Hi!!
If i solve it as you said, i again get (a) option.

14. Jul 30, 2011

Saitama

But what's the correct method?

15. Jul 30, 2011

I like Serena

My apologies pmsrw3, it was not my intention to interfere, so I deleted my post.

16. Jul 30, 2011

pmsrw3

That's it. If you try a bunch of calculations, it should become obvious that when n is big, n is practically the same as n+1, and 2n is practically the same as 2n+1.

17. Jul 30, 2011

Saitama

Thank you so much, i got it!!

18. Jul 30, 2011

I like Serena

Well, there is a catch...
What happens if you apply this estimation rule to your equation?

19. Jul 30, 2011

Saitama

It becomes zero. :surprised

20. Jul 30, 2011

I like Serena

Any idea why?
And how you should handle it?

21. Jul 30, 2011

Saitama

No idea.

22. Jul 30, 2011

I like Serena

Well, if you subtract 2 almost equal large quantities, the result is small but not zero.
This is something you can not neglect.
So (n+1) - n = 1 and this is not 0.

The trick is to eliminate subtractions, before you neglect stuff.

23. Jul 30, 2011

Saitama

Thanks for clarification!!
Can you please see to the thread "Atomic Structure Question" in "other Science".
tiny-tim replied that i should first find out the force, but i have never dealt with force in atomic structure.