How to calculate frequency and wavelength - please help w. questions?

Question1:

** Answer in units of s^-1

What is the frequency of the 436 nm violet light emitted by the mercury atoms in a fluorescent light bulb?

All electromagnetic radiation, including visible light, travels at about 300,000,000 metres per second in a vacuum.

Ie 300,000,000 ms^-1 = 3 *10^8 m/s

Now light can be thought of as a propagating energy wave.

The frequency of the radiation is the time taken for one cycle to complete. That is for one wavelength to pass by a fixed point. (We won’t go into relativity effects!!)

Look at the units of velocity they are Metres divide by seconds m/s

and your answer needs to be in 1/s

So to do this we must divide the velocity by a length, something in metres to make m/s into 1/s

You are given the wavelength of the light as 436 nm that is 436 nano metres = 436 x 10^-9 metres

So Frequency = Velocity / Wavelength (m/s )/m = s^-1

Frequency = 3 * 10^8/436 x 10^-9 s^-1 (Lengths must all be in the same units. Say Metres)

Frequency = 3 /436 * 10^17 cycles per second or just s^-1

= 6.881 * 10^-3 * 10^17

= 6.881 * 10^14 s^-1

Question 2:

**Answer in units of meters.

Calculate the wavelength of radiation with a frequency of 5.2 x10^14 per second.

Wavelength = Velocity / Frequency (m/s)*s = m

Wavelength = 3 * 10^8/ [5.2 *10^14 ]

= 3/5.2 * 10^-6

= 0.5769 * 10^-6 m <- Answer in Metres

= 0.5769 * 10^-6 *10^9 nm

= 0.5769 * 10^3 nm

= 5769 nm (this is emerald green)