Question

Yellow light emitted from a sodium lamp has a wavelength (λ) of 580 nm. Calculate the frequency (ν) and wavenumber (ν ) of the yellow light.
___________________________
$chemistry \:$
$class \: 11th$

__________________

$kindly \: give \: accurate \: answer \:$
♡ karishma~​

Answer 1

Answer:

Wavenumber = 1/wavelength = 1/580 nm = $\frac{1}{580X 10^{-9}} = 1.7 X 10^6m^{-1}$

Frequency = Velocity/ Wavelength = $\frac{3X 10^8}{580X10^{-9}} = 5.1 X 10^{14} Hz$

Answer 2

$\Large{\textsf{\textbf{\underline{\underline{Given\::}}}}}$

• Wavelength (λ) of a yellow light is 580 nm.

$\Large{\textsf{\textbf{\underline{\underline{To\:do\::}}}}}$

1. The frequency of the yellow light.
2. Wavenumber of the yellow light.

$\Large{\textsf{\textbf{\underline{\underline{Solution\::}}}}}$

As we know that,

The formula to calculate frequency of the yellow light is,

$\orange\bigstar\:{\Large\mid}\:\bf\purple{Frequency\:(\nu)\:=\:\dfrac{c}{\lambda}\:}\:{\Large\mid}\:\green\bigstar$

Where,

• c = speed of light = 3 × 10⁸ m/s

• λ = 580 nm = $\tt{580\times{10^{-9}}\:m}$

$\dashrightarrow\:\tt{\nu\:=\:\dfrac{3\times{10^{8}}}{580\times{10^{-9}}}\:}$

$\dashrightarrow\:\tt{\nu\:=\:0.0051\times{10^{8}}\times{10^{9}}\:}$

$\dashrightarrow\:{\bf{\pink{\nu\:=\:0.0051\times{10^{17}}\:sec^{-1}\:}}}$

Again,

The formula to calculate the wavenumber of the yellow light is,

$\orange\bigstar\:{\Large\mid}\:\bf\blue{Wavenumber\:(\overline{\nu})\:=\:\dfrac{1}{\lambda}\:}\:{\Large\mid}\:\green\bigstar$

$\dashrightarrow\:\tt{\overline{\nu}\:=\:\dfrac{1}{580\times{10^{-9}}}\:}$

$\dashrightarrow\:{\bf{\pink{\overline{\nu}\:=\:0.0017\times{10^{9}}\:m^{-1}\:}}}$