Question

Visible light has wavelengths ranging from 400 nm (violet) to 750 nm (red). Express these wavelengths in terms of frequency (Hz). (1 nm = 10^-9m)

Answer 1

Given : 

Wavelengths : 

λ₁ = 400 nm (for violet light), 

λ₂ = 750 nm (for red light) 

To find : 

Frequencies : ν₁, ν₂

Formula : 

ν = \(\frac{c}{\lambda}\) 

Calculation : 

i. Wavelength of violet light, 

λ₁ = 400 nm = 400 × 10^-9 m

Frequency,

ν = \(\frac{c}{\lambda}\) 

Where c is speed of light = 3.0 × 10⁸ms^-1

∴ ν₁ = \(\frac{3.0\times 10^8 ms^{-1}}{400\times 10^{-9}m}\)

= 7.50 × 10¹⁴Hz

ii. Wavelength of red light, 

λ₂ = 750 nm = 750 × 10^-9m

Frequency,

ν = \(\frac{c}{\lambda}\) 

∴ ν₂ = \(\frac{3.0\times 10^8\,m\,s^{-1}}{750\times 10^{-9}\,m}\) 

= 4.00 × 10¹⁴ Hz

The frequency of violet light is 7.50 × 10¹⁴ Hz and that of red light is 4.00 × 10¹⁴ Hz.