Answer:
Information shadow: In the above problem, the
wavelength of yellow-coloured radiation is given, while frequency and wave
number are required.
\[\lambda
=5800\overset{{}^\circ }{\mathop{\text{A}}}\,\]
\[=5800\times
{{10}^{-10}}m\] (i)
Velocity
of light may be taken as,
\[c=3\times
{{10}^{8}}m\,{{\sec }^{-1}}\] (ii)
Problem solving strategy: In the
problem, wave number and frequency are required which can be calculated using
following relations,
\[\overset{\_}{\mathop{v}}\,=\frac{1}{\lambda
}\] (iii)
Frequency, \[v=\frac{c}{\lambda
}\] .(iv)
Working it out:
From equation (iii), \[\overset{\_}{\mathop{v}}\,=\frac{1}{5800\,\overset{{}^\circ
}{\mathop{\text{A}}}\,}\]
\[\overset{\_}{\mathop{v}}\,=\frac{1}{5800\,\times
{{10}^{-10}}}\] \[(1\,\overset{{}^\circ }{\mathop{A}}\,={{10}^{-10}}m)\]
\[=1.724\times
{{10}^{6}}\,{{m}^{-1}}\]
From equation (iv), \[v=\frac{c}{\lambda
}=\frac{3\times {{10}^{8}}}{5800\times {{10}^{-10}}}\]
\[=5.172\times {{10}^{14}}Hz\]
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