Question

Calculate (a) wavenumber and (b) frequency of yellow radiation with wavelength 5800 $\mathring{A}$.

• A. 1.724 x 10⁴ cm^-1 and5.172 x 10¹² s^-1
• B. 1.724 x 10⁴ cm^-1 and 5.172 x 10¹⁴ s^-1
• C. 1.724 x 10¹² cm^-1 and 5.172 x 10⁴ s^-1
• D. 1.724 x 10¹² cm^-1 and 5.172 x 10² s^-1

Answer 1

The correct option is B

1.724 x 10⁴ cm^-1 and 5.172 x 10¹⁴ s^-1

We know that:
$\overline{v}=\frac{1}{\lambda }and{v}^{-}=\frac{c}{\lambda }$
Now, calculation of wave number $\left(\overline{v}\right)$
$\Lambda =5800\mathring{A}=5800\times {10}^{-8}cm$
$=5800\times {10}^{-10}m$
$\overline{v}=\frac{1}{\lambda }=\frac{1}{5800\times {10}^{-10}m}$
$=1.724\times {10}^6{m}^{-1}$
$=1.724\times {10}^{4}c{m}^{-1}$
Calculating frequency(v)
$v=\frac{c}{\lambda }=\frac{3\times {10}^{8}m{s}^{-1}}{5800\times {10}^{-10}m}$
=$5.172\times {10}^{14}{s}^{-1}$