Question

The wavelength range of the visible spectrum extends from violet (400 nm) to red (750 nm). Express these wavelength in frequencies (Hz). $(1nm={10}^{-9}m)$.

• A. 4 x 10¹⁴ to 7.5 x 10¹⁴ Hz
• B. 8 x 10¹⁴ to 16 x 10¹⁴ Hz
• C. 7 x 10¹⁴ to 16 x 10¹⁴ Hz
• D. 7.5 x 10¹⁴ to 16 x 10¹⁴ Hz

Answer 1

The correct option is A

4 x 10¹⁴ to 7.5 x 10¹⁴ Hz

We know that,
$v=\frac{c}{\lambda }$
Now, frequency of violet light is:
$v=\frac{c}{\lambda }=\frac{3.00\times {10}^{8}m{s}^{-1}}{400\times {10}^{-9}m}$
$=7.50\times {10}^{14}Hz$

Frequency of red light is:
$v=\frac{c}{\lambda }=\frac{3.00\times {10}^{8}m{s}^{-1}}{750\times {10}^{-9}m}$
$=4.00\times {10}^{14}Hz$

The range of the visible spectrum is from $4.0\times {10}^{14}Hz$ to $7.50\times {10}^{14}Hz$.