Question

The frequency range of visible light is from 3.75 × 10¹⁴ Hz to 7.5 × 10¹⁴ Hz. Calculate its wavelength range. Take speed of light = 3 × 10⁸ m/s.

Answer 1

Frequency f = 3.75 × 10¹⁴ Hz

Velocity of light (C) = 3 × 10⁸ m/s

λ = `C/f`

= `(3 xx 10^8)/(3.75 xx 10^14)`

= `(3000 xx 10^5)/(375 xx 10^12)`

λ = `(8 xx 10^5)/(10^12)`

= `8 × 10^(5 - 12)`

= 8 × 10^-7 m

= 8 × 10^-7 × 10¹⁰ Å

= `8 × 10^(-7+10)`

= 8 × 10³ Å

Also, f = 7.5 × 10¹⁴ Hz

λ = `C/f`

= `(3 xx 10^8)/(7.5 xx 10^14)` m

= `(3 xx 10^8)/(75 xx 10^13)` m

= `(300)/(75) xx (10^6)/(10^13)`

= `4 × 10^(6 - 13)`m

= 4 × 10^-7

= `4 xx 10^(-7 + 10)`

= 4 × 10³

= 4000 Å

∴ Wavelength range of visible light is 4000 Å to 8000 Å