Question

the yellow light given off by sodium has a frequency of 5.09×10‐¹⁴ s-¹ . calculate the wavelength of this light in nanometers​

Answer 1

The frequency of the yellow light given off by sodium is,

$\longrightarrow\sf{\nu=5.09\times10^{-14}\ s^{-1}}$

We know the speed of light is,

$\longrightarrow\sf{v=3\times10^8\ m\,s^{-1}}$

The wavelength of the light is given by,

$\longrightarrow\sf{\lambda=\dfrac{v}{\nu}}$

$\longrightarrow\sf{\lambda=\dfrac{3\times10^8}{5.09\times10^{-14}}}$

$\longrightarrow\sf{\lambda=5.9\times10^{21}\ m}$

But we need wavelength in nanometer.

$\longrightarrow\sf{\lambda=5.9\times10^{21+9-9}\ m}$

$\longrightarrow\sf{\lambda=5.9\times10^{30-9}\ m}$

$\longrightarrow\sf{\lambda=5.9\times10^{30}\times10^{-9}\ m}$

$\longrightarrow\underline{\underline{\sf{\lambda=5.9\times10^{30}\ nm}}}$