Question

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

Answer 1

Hint: In the given question, the wavelength range of the visible spectrum from violet to red is given where the frequency of the waves is calculated by dividing the speed of light by the wavelength given. The speed of light is equal to $3 \times {10^8}m{s^{ - 1}}$.

Complete step by step answer:
Given,
The wavelength range of violet is 400 nm.
The wavelength range of red is 750 nm.
1 nm is ${10^{ - 9}}$m
The frequency is defined as the number of waves that pass a certain point in a certain amount of time.
The frequency of the light is calculated by dividing the speed of light by the wavelength.
The formula for calculating the frequency is shown below.
$f = \dfrac{c}{\lambda }$
Where
f is the frequency
c is the speed of light
$\lambda$ is the wavelength
The value of speed of light is $3 \times {10^8}m{s^{ - 1}}$
To calculate the frequency of violet light, substitute the values of speed of light and wavelength in the above equation.
$\Rightarrow f = \dfrac{{3 \times {{10}^8}}}{{400 \times {{10}^{ - 9}}}}$
$\Rightarrow f = 7.50 \times {10^{14}}Hz$
The unit of hertz is inverse second.
Therefore, the wavelength in frequency of violet light in hertz is $7.50 \times {10^{14}}$ Hz or $7.50 \times {10^{14}}$${s^{ - 1}}$
To calculate the frequency of red, substitute the values of speed of light and wavelength in the above equation.
$\Rightarrow f = \dfrac{{3 \times {{10}^8}}}{{750 \times {{10}^{ - 9}}}}$
$\Rightarrow f = 4 \times {10^{14}}Hz$
Therefore, the wavelength of frequency of red light in hertz is $4 \times {10^{14}}Hz$ or $4 \times {10^{14}}$${s^{ - 1}}$.

Note:
Make sure to convert the value of wavelength in nanometers into meters as the speed of light is given in meters per second. 1 nanometer is equal to ${10^9}$ m.