Question.
Calculate the wavelength, frequency and wave number of a light wave whose period is $2.0 \times 10^{-10} \mathrm{~s} .$
Calculate the wavelength, frequency and wave number of a light wave whose period is $2.0 \times 10^{-10} \mathrm{~s} .$
Solution:
Frequency $(v)$ of light $=\frac{1}{\text { Period }}$
$=\frac{1}{2.0 \times 10^{-10} \mathrm{~s}}=5.0 \times 10^{9} \mathrm{~s}^{-1}$
Wavelength $(\lambda)$ of light $=\frac{c}{v}$
Where
$c=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
Substituting the value in the given expression of $\lambda$ :
$\lambda=\frac{3 \times 10^{8}}{5.0 \times 10^{9}}=6.0 \times 10^{-2} \mathrm{~m}$
Wave number $(\bar{v})$ of light $=\frac{1}{\lambda}=\frac{1}{6.0 \times 10^{-2}}=1.66 \times 10^{1} \mathrm{~m}^{-1}=16.66 \mathrm{~m}$
Frequency $(v)$ of light $=\frac{1}{\text { Period }}$
$=\frac{1}{2.0 \times 10^{-10} \mathrm{~s}}=5.0 \times 10^{9} \mathrm{~s}^{-1}$
Wavelength $(\lambda)$ of light $=\frac{c}{v}$
Where
$c=$ velocity of light in vacuum $=3 \times 10^{8} \mathrm{~m} / \mathrm{s}$
Substituting the value in the given expression of $\lambda$ :
$\lambda=\frac{3 \times 10^{8}}{5.0 \times 10^{9}}=6.0 \times 10^{-2} \mathrm{~m}$
Wave number $(\bar{v})$ of light $=\frac{1}{\lambda}=\frac{1}{6.0 \times 10^{-2}}=1.66 \times 10^{1} \mathrm{~m}^{-1}=16.66 \mathrm{~m}$