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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.
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Solution
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
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