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A mercury lamp emits radiation with a frequency of 6.83 x 1014 Hz. What is the wavelength of this radiation?

Fill in the blanks as you answer the question. Remember to include units. (If you need to write a superscript, put a ^ before the number to be superscripted. For example, x2 would be written as x^2.)

Step 2: What is the speed of light to four significant figures?

Step 3: What is the frequency of the light from the mercury lamp?

Step 4: What is the wavelength of the light from the mercury lamp? blank space 3

Light behaves like a wave. The wavelength of a wave is equal to the distance that it travels (in the given medium) in each period of oscillation.

On the other hand, the frequency of a wave is the number of periods in unit time. [tex]1\rm \; Hz[/tex] means one oscillation per second. The frequency of this particular wave is [tex]\rm 6.83\times 10^{14}\; Hz[/tex]. In other words, there are [tex]6.83\times 10^{14}[/tex] oscillations in each second.

The period of oscillation will be equal to

[tex]\displaystyle t = \frac{1}{f} = \frac{1}{\rm 6.83\times 10^{14}\; s^{-1}}[/tex].

In that period of time, a beam of light in vacuum would have traveled

[tex]\displaystyle \rm 2.998\times 10^{8}\; m\cdot s^{-1} \times \frac{1}{\rm 6.83\times 10^{14}\; s^{-1}} = 4.39\times 10^{-7}\; m[/tex].

In other words, if this beam of light of frequency [tex]\rm 6.83\times 10^{14}\; Hz[/tex] is in vacuum, its wavelength will be equal to [tex]\rm 4.39\times 10^{-7}\; m[/tex].