Atomic Structure Question 470
Question: Let $ v_1 $ be the frequency of the series limit of the Lyman series, $ v_2 $ be the frequency of the first line of the Lyman series, and $ v_3 $ be the frequency of the series limit of the Balmer series, then
Options:
A) $ v_3=\frac{1}{2}(v_1-v_3) $
B) $ v_2-v_1=v_3 $
C) $ v_1-v_2=v_3 $
D) $ v_1+v_2=v_3 $
Show Answer
Answer:
Correct Answer: C
Solution:
- $ v_1=Rc,Z^{2}( \frac{1}{n_1^{2}}-\frac{1}{n_2^{2}} ) $ $ v_1=Rc,Z^{2}( \frac{1}{1^{2}}-\frac{1}{{{\infty }^{2}}} )=Rc,Z^{2} $ $ v_2=Rc,Z^{2}( \frac{1}{1^{2}}-\frac{1}{2^{2}} )=\frac{3,Rc,Z^{2}}{4} $ $ v_3=Rc,Z^{2}( \frac{1}{2^{2}}-\frac{1}{{{\infty }^{2}}} )=\frac{2,Rc,Z^{2}}{4} $
$ \therefore $ $ v_1-v_2=v_3 $
