Question

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

• A. $1.724\times {10}^{4}c{m}^{-1}and5.172\times {10}^{12}{s}^{-1}$
• B. $1.724\times {10}^{4}c{m}^{-1}and5.172\times {10}^{14}{s}^{-1}$
• C. $1.724\times {10}^{12}c{m}^{-1}and5.172\times {10}^4{s}^{-1}$
• D. $1.724\times {10}^{12}c{m}^{-1}and5.172\times {10}^2{s}^{-1}$

Answer 1

Answer: (B)

Step 1:

$\overline{v}=\frac{1}{\lambda }and\nu =\frac{c}{\lambda }$
Now, for the calculation of wave number $\left(\overline{v}\right)$
$\Lambda =5800\mathring{A}=5800\times {10}^{-8}cm$
$=5800\times {10}^{-10}m$

Step 2:
$\overline{v}=\frac{1}{\lambda }=\frac{1}{5800\times {10}^{-10}m}$
$=1.724\times {10}^6{m}^{-1}$
$=1.724\times {10}^{4}c{m}^{-1}$
Calculating of the frequency(v)

Step 3:
$\nu =\frac{c}{\lambda }=\frac{3\times {10}^{8}m{s}^{-1}}{5800\times {10}^{-10}m}$
=$5.172\times {10}^{14}{s}^{-1}$

Hence, option (D) is correct.