how can you test to see if a light with wavelength 413nm is the same light with a frequency of 6.26*10^14Hz?

6.26E14 x 413E-9 = ? and compare with c = 3E8.

distance = speed * time

and
period = 1/f

413 *10^-9 meters ?=?? 3*10*8 m/s / (6.26 * 10^14)

413 * 10^-9 = .479 *10^-6 ????

413 = 478 ???
not really

To test if a light with a wavelength of 413 nm is the same light with a frequency of 6.26 * 10^14 Hz, we can use the formula relating wavelength and frequency:

c = λν

where c is the speed of light, λ is the wavelength, and ν is the frequency.

1. First, we need to convert the given wavelength from nanometers to meters. Since 1 nm = 1 x 10^-9 m, the wavelength becomes:

λ = 413 nm * (1 x 10^-9 m/1 nm) = 413 x 10^-9 m = 4.13 x 10^-7 m

2. Next, we substitute the values of the wavelength and frequency into the formula to check if they are consistent:

c = λν
3.00 x 10^8 m/s = (4.13 x 10^-7 m)(6.26 x 10^14 Hz)

3. Calculate the right side of the equation:

(4.13 x 10^-7 m)(6.26 x 10^14 Hz) = 2.5838 x 10^8

Now we compare this value to the speed of light, 3.00 x 10^8 m/s:

2.5838 x 10^8 ≈ 3.00 x 10^8

Since the numbers are approximately equal, we can conclude that the light with a wavelength of 413 nm and a frequency of 6.26 x 10^14 Hz represents the same light.