Question

1. The wavelength of a violet light is 400 nm. Calculate the frequency and wavenumber.

Answer 1

Given:

The wavelength of a violet light $(\lambda)$ = 400 nm = 400 × $10^{-9}$ m

We have to calculate the frequency($\nu$$\nue$) and wave number.

Solution:

∴ Frequency($\nu$$\nue$) = $\dfrac{c}{\lambda}$

Where, c = velocity of light = 3 × $10^{8}$ m

Frequency($\nu$$\nue$) = $\dfrac{3\times 10^{8} }{400\times 10^{-9} }$

= $\dfrac{3\times 10^{8} }{400\times 10^{-9} }$

= 0.0075 × $10^{17}$ Hz

= 7.5 × $10^{14}$ Hz

Also,

Wave number = $\dfrac{1}{\lambda}$

= $\dfrac{1}{400\times 10^{-9} }$

= 0.0025 × $10^{9}$ $m^{-1}$

= 2.5 × $10^{6}$ $m^{-1}$

∴ Frequency($\nu$$\nue$) = 7.5 × $10^{14}$ Hz and

Wave number = 2.5 × $10^{6}$ $m^{-1}$

Answer 2

Given:

The wavelength of the violet light = 400nm

To find:

The frequency and the wave number of the violet light used.

Solution:

The frequency is given as: f = c/λ

Where c is the speed of light in vacuum. Therefore:

f = 3*10⁸ / 400*10⁻⁹ = 7.5*10¹⁴ Hz

Wave number is given as: w= 1/λ

w = 1/ 400*10⁻⁹ = 2.5*10⁶ m⁻¹

Therefore the frequency of the violet light is 7.5*10¹⁴ Hz and its wave number is 2.5*10⁶ m⁻¹.