Blue light had a frequency of 6.98*10^14 hertz. what is the wavelength of blue light in nanometers? ? why? ?

This can be answered using the wave equation. Since all light travels at 299 792 458 m/s and we know the frequency the equation can be rearranged to solve for wavelength. (steps shone below). Remember the Universal Wave Equation which is v=fλ; where v=speed, f=frequency, and λ=wavelength

1)v=fλ (universal wave equation)
2) v/f=λ (rearrange the equation 
3) 299 792 458/6.98x10^14=λ (plug in the known values and enter into a calculator; when typing in the 6.98x10^14 make sure to use the EXP or EE key on your calculator in place of the x10: 6.98x10^14 would be typed in as 6.98E14, if this is not done then you can just bracket the 6.98x10^14 instead.)
4) 4.2950...x10^-7=λ (solve for λ)
5) 4.3x10^-7=λ (round, in this case i rounded to the nearest hundredth)
6) Therefore the answer is 4.3x10^-7 m.

However, you must convert the answer stated above into nm. This will be done through unit conversion. I dont know if you have learned unit conversion but i will demonstrate it below.
 
Step 1) Write out the ratio of the prefix (in this case the only prefix is "nano")
                 1 nm.= 1x10^-9 m

Step 2) This is difficult to explain so I will just write it out and if you have any questions feel free to ask.

1nm/1x10^-9m*4.3x10^-7 m.=?nm.
This is equal to 430 nm.

Therefore, the wavelength of the Blue Light is about 430 nm.
(Ideally you wouldn't do any rounding til the very end however I was not in access of a proper calculator so I did the rounding right away)

The reason why would be because in order for the Blue light to travel the speed of light then the wavelength would need to be about 430 nm. b/c of the fact it will travel 430 nm. for every wavelength (which is represented by the frequency; which is number of cycles in 1 second) Therefore the wavelength must be about 430 nm. so the blue light will travel at the speed of light. 

 

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