Atoms And Nuclei Question 318
Question: The ratio of minimum to maximum wavelengths of radiation that an excited electron in a hydro- gen atom can emit while going to the ground state is
Options:
A) 1/2
B) Zero
C) 3/4
D) 27/32
Show Answer
Answer:
Correct Answer: C
Solution:
- E is minimum when $ n_{1}=1\And n_{2}=2 $
$ \Rightarrow {E_{\min }}=13.6( \frac{1}{1}-\frac{1}{4} )eV=13.36\times \frac{3}{4}eV $ E is maximum when $ n_{1}=1\And n_{2}=\infty $ (the atom is ionized, that is known as ionization energy)
$ \Rightarrow {E_{\min }}=13.6( 1-\frac{1}{\infty }=13.6eV ) $
$ \therefore \frac{{E_{\min }}}{{E_{\max }}}=\frac{3}{4}\Rightarrow \frac{hc/{\lambda_{\max }}}{hc/{\lambda_{\min }}}=\frac{3}{4}\Rightarrow \frac{{\lambda_{\max }}}{{\lambda_{\min }}}=\frac{3}{4} $
