Question

Calculate the frequency, wave number of the microwaves with wavelength 4 x 107 nm.​

Answer 1

Answer:

Frequency = ν = 7.5 * 10⁻⁹ s⁻¹

Wave number = $\bar{\nu}$ = 1.33 * 10⁹ m⁻¹

Explanation:

$\diamond$ We know that,

$\implies$ Speed of light = Frequency * Wavelength

$\implies$ c = νλ

$\diamond$ We also know that,

$\implies$ Wave number = $\dfrac{1}{Wavelength}$

$\implies$ $\bar{\nu}$ = $\dfrac{1}{\lambda}$

$\diamond$ Given that,

$\implies$ Wavelength = λ = 4 * 10⁷ nm = 4 * 10¹⁶ m

$\implies$ Speed of light = c = 3 * 10⁸ m/s

$\diamond$ Substituting the value of ν and c in c = νλ we get,

$\implies$ 3 * 10⁸ = λ * 4 * 10¹⁶

$\implies$ λ = 0.75 * 10⁻⁸

$\implies$ λ = 7.5 * 10⁻⁹ s⁻¹

$\diamond$ Substituting the value of λ in $\bar{\nu}$ = $\dfrac{1}{\lambda}$ we get,

$\implies$ $\bar{\nu}$ = $\dfrac{1}{7.5 * 10^{-9}}$

$\implies$ $\bar{\nu}$ = 1.33 * 10⁹ m⁻¹