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} $


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