Atomic Structure - Result Question 110
####86. The electron energy in hydrogen atom is given by $E _n=-\frac{21.7 \times 10^{-12}}{n^{2}}$ erg. Calculate the energy required to remove an electron completely from the $n=2$ orbit. What is the longest wavelength (in $cm$ ) of light that can be used to cause this transition?
(1984, 3M)
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Solution:
- The required transition is $n _1=2$ to $n _2=\infty$ and corresponding transition energy is
$$ \begin{aligned} \Delta E & =21.7 \times 10^{-12}\left(\frac{1}{n _1^{2}}-\frac{1}{n _2^{2}}\right) erg \ & =\frac{21.7}{4} \times 10^{-12} erg=5.425 \times 10^{-12} erg \end{aligned} $$
The longest wavelength that can cause above transition can be determined as :
$$ \begin{aligned} \lambda & =\frac{h c}{\Delta E}=\frac{6.625 \times 10^{-34} \times 3 \times 10^{8}}{5.425 \times 10^{-12} \times 10^{-7}} \ & =3.66 \times 10^{-7} m=3.66 \times 10^{-5} cm \end{aligned} $$
