Atomic Structure - Result Question 111
####87. Calculate the wavelength in Angstroms of the photon that is emitted when an electron in the Bohr’s orbit, $n=2$ returns to the orbit, $n=1$ in the hydrogen atom. The ionisation potential of the ground state hydrogen atom is $2.17 \times 10^{-11}$ erg per atom.
(1982, 4M)
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Solution:
- Ionisation potential of $H$-like species
$$ =E _1=2.17 \times 10^{-11} erg $$
$$ \begin{aligned} \Rightarrow \quad \Delta E & =2.17 \times 10^{-11}\left(1-\frac{1}{2^{2}}\right) \times 10^{-7} J \ & =1.6275 \times 10^{-18} J \Rightarrow \lambda=\frac{h c}{\Delta E} \ & =\frac{6.625 \times 10^{-34} \times 3 \times 10^{8}}{1.6275 \times 10^{-18}} m \ & =122 \times 10^{-9} m=1220 \AA \end{aligned} $$
