Atoms And Nuclei Question 312
Question: In the hydrogen atom spectrum $ {\lambda_{3-1}} $ and $ {\lambda_{2-1}} $ represent wavelengths emitted due to transition from second and first excited states to the ground. state respectively. The value of $ \frac{{\lambda_{3-1}}}{{\lambda_{2-1}}} $ is
Options:
A) 27/32
B) 32/27
C) 4/9
D) 9/4
Show Answer
Answer:
Correct Answer: A
Solution:
- $ \frac{1}{{\lambda_{3-1}}}=R( \frac{1}{1^{2}}-\frac{1}{3^{2}} )=\frac{8R}{9} $ $ \frac{1}{{\lambda_{2-1}}}=R( \frac{1}{1^{2}}-\frac{1}{2^{2}} )=\frac{3R}{4}\Rightarrow \frac{{\lambda_{3-1}}}{{\lambda_{2-1}}}=\frac{27}{32} $
