Answer:
Information shadow: In this problem, energy levels
of transition and the name of element are given.
\[{{n}_{2}}=5\] (higher energy
level) ...(i)
\[{{n}_{1}}=2\](lower energy
level) ...(ii)
Atomic number of the element
(hydrogen), i.e., Z = 1
Problem solving strategy:
When transition of electrons takes place from higher level to lower level, the
energy is released in the form of electromagnetic radiation. The wavelength of emitted
radiation can be calculated using following Rydberg equation
\[\frac{1}{\lambda
}=R{{Z}^{2}}\left[ \frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}} \right]\] (i)
where R = Rydberg's
constant ...(iv)
\[=109677.76c{{m}^{-1}}\]
Working it out: Substituting the
values of \[{{n}_{1}},{{n}_{2}}\], R and Z in equation (iii), we get
\[\frac{1}{\lambda
}=109677.76\times {{1}^{2}}\left[ \frac{1}{{{2}^{2}}}-\frac{1}{{{5}^{2}}}
\right]\]
\[\lambda =4.34\times
{{10}^{-5}}cm\]
\[\lambda =4.34\times
{{10}^{-9}}m\]
\[\lambda =4.34nm\]
Frequency \[v=\frac{c}{\lambda }=\frac{3\times
{{10}^{8}}}{434\times {{10}^{-9}}}=6.91\times {{10}^{14}}Hz\]
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