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 x 10⁸ m s^-1

As we know,

Speed of light (c) = Frequency (f) x Wavelength (λ)

Given,

C = 3 x 10⁸ m s^-1

Frequency range = 3.75 × 10¹⁴ Hz to 7.5 × 10¹⁴ Hz.

Let, f₁ = 3.75 × 10¹⁴ Hz

Substituting the values in the formula,

$3 \times 10^8 = 3.75 × 10^{14} \times λ \\[0.5em] \text {λ} = \dfrac {3 \times 10^8 }{3.75 × 10^{14}} \\[0.5em] \Rightarrow \text {λ} = 0.8 \times 10^{-6} \text {m} \\[0.5em] \Rightarrow \text {λ} = 8000 \times 10^{-10} \text {m} \\[0.5em]$

As, 1 Å = 10^-10 m

Therefore,

λ₁ = 8000 Å

Let, f₂ = 7.5 × 10¹⁴ Hz

Substituting the values in the formula,

$3 \times 10^8 = 7.5 × 10^{14} \times λ \\[0.5em] \text {λ} = \dfrac {3 \times 10^8 }{7.5 \times 10^{14}} \\[0.5em] \Rightarrow \text {λ} = 0.4 \times 10^{-6} \text {m} \\[0.5em] \Rightarrow \text {λ} = 4000 \times 10^{-10} \text {m} \\[0.5em]$

As, 1 Å = 10^-10 m

Therefore,

λ₂ = 4000 Å

Therefore, the wavelength range is 4000 Å to 8000 Å.