Question

The wavelength of light emitted from a traffic light having a frequency of 5.97×1014 Hz is ________ nm.

Answer 1

To calculate the wavelength of light from a traffic light with a frequency of 5.97×1014 Hz, use the relationship λ = c/f, where c is the speed of light. The calculated wavelength is 502.5 nm.

Step-by-step explanation:

The wavelength of light emitted from a traffic light having a frequency of 5.97×1014 Hz can be determined using the formula for wave speed, which is the product of frequency (f) and wavelength (λ). The speed of light (c) is a constant at approximately 3.0×108 m/s. Therefore, we can rearrange the formula to solve for wavelength (λ = c/f).

Firstly, convert the speed of light into nm/s to match the units of our final answer, knowing that 1 m = 1×109 nm:

c = 3.0×108 m/s = 3.0×1017 nm/s.

Now, we can calculate the wavelength:

λ = c/f = 3.0×1017 nm/s / 5.97×1014 Hz = 502.5 nm.

So, the wavelength of light emitted from the traffic light is 502.5 nm.

Answer 2

First, we have to remember the equation that relates the wavelength with the frequency:

`v=\text{ }\lambda* f`

In which v is the wave speed, lambda is the wavelength and f is the frequency.

From this equation, we can reformulate it as:

`\lambda=\text{ }(v)/(f)`

Now, we know that the light speed is 3x108 m/s, so we can replace in the previous equation:

`\lambda=\text{ }\frac{3*10^8\text{ m/s}}{5.97*10^(14)Hz}=\text{ 5.025}*10^(-7)\text{ m = 502.51 nm}`

So, the answer is 502.51 nm