Question 1.15

$c=\lambda v$

Cassidy 1G
Posts: 54
Joined: Fri Sep 29, 2017 7:07 am

Question 1.15

Hi, I can't figure out problem 1.15 from the textbook. The problem says "In the ultraviolet spectrum of atomic hydrogen, a line is observed at 102.6 nm. Determine the values of n for the initial and final energy levels of the electron during the emission of energy that leads to this spectral line." I think we use the Rydberg equation for this, but I don't really know what to do.

Andrea Grigsby 1I
Posts: 60
Joined: Fri Sep 29, 2017 7:03 am

Re: Question 1.15

1. convert the wavelength given to m
102.6x10^-9m

2. figure out the frequency by rearranging c=wavelength*frequency
v=c/wavelength
= 2.998*10^8 / 102.6*10^-9
= 2.922x10^15

3. as the question says "in the ultraviolet spectrum", one can concur that the final energy level is n=1

4. put known values into the Rydberg equation
2.922x10^15 = 3.29*10^15 (1 - (1/n^2))
(rydberg constant ^) (^ because 1/1^2 = 1)

5. rearrange the equation to solve for n
(1- (1/n^2)) = 0.888
1/n^2 = 1 - 0.888
= 0.112
n^2 = 9
n = 3(initial energy level)

Annie Lieu-1H
Posts: 68
Joined: Fri Sep 29, 2017 7:04 am
Been upvoted: 1 time

Re: Question 1.15

For the Rydberg equation, you're missing the frequency. So first, you need to find the frequency using the given wavelength. Find this using the c=wavelength*frequency formula. You can then use the calculated frequency for the Rydberg equation! (Remember that for these type of problems, if they don't give you the n1 level, then it's implied to be 1). After that, it's algebraic calculations! Hope this helps