Question

If the frequency is 5 into 10 ^ 15 then what is the wavelength and wavenumber

Answer 1

$\large\underline{\bigstar{\sf Given-}}$

• Frequency (f) = ${\sf 5×10^{15}\:Hz}$

$\large\underline{\bigstar{\sf To \: Find-}}$

• Wavelength
• Wave number

$\large\underline{\bigstar{\sf Formula \: Used-}}$

$\color{violet}\bullet\underline{\boxed{\sf Frequency (\nu)=\dfrac{c}{\lambda}}}$

$\color{violet}\bullet\underline{\boxed{\sf Wave\:number\:(k)= \dfrac{1}{\lambda}}}$

$\large\underline{\bigstar{\sf Solution-}}$

★ Wavelength

$\implies{\sf \nu=\dfrac{c}{\lambda}}$

c = speed of light $\implies{\sf 3×10^8\:m/s}$

$\implies{\sf \lambda=\dfrac{3×10^8}{5×10^{15}} }$

$\implies{\sf \lambda = 0.6×10^{-7}\:m }$

$\color{red}\implies{\sf \lambda = 6×10^{-8}\:m }$

_______________________________

★ Wave Number (k)

$\implies{\sf k =\dfrac{1}{\lambda}}$

$\implies{\sf k=\dfrac{1}{6×10^{-8}}}$

$\implies{\sf k=0.16×10^{8}}$

$\color{red}\implies{\sf k= 16×10^6\ }$

$\large\underline{\bigstar{\sf Answer-}}$

Wavelength = $\color{red}{\sf 6×10^{-8}\:m}$

Wave Number = $\color{red}{\sf 16×10^6}$