Light Waves and Colors Legacy Problem #6 Guided Solution
Problem*
Determine the frequency of … (GIVEN: 1 m = 109 nm)
- Red visible light (λ = 650 nm)
- Violet visible light (λ = 420 nm)
Audio Guided Solution
In this problem we wish to calculate the frequency of two portions of the visible light spectrum. We wish to calculate the frequency of red light, which has a wavelength of 650 nm, and then of violet light, which has a wavelength of 420 nm. In order to calculate the wavelength, we need to use the wave equation v equals f times lambda, where v is the speed, f is the frequency, and lambda is the wavelength. So rearranging to solve for frequency, we would have f equal v divided by lambda. The v value is 2.998 times 10 to the 8th meters per second. We need to divide that by the wavelength, but we should have it in units of meters. So the 650 nm can be converted to meters by dividing by 10 to the 9th nm per meter. That becomes 6.5 times 10 to the negative 7th meters. Now we can divide that into the speed of light, and we can get the frequency for the red visible light. It comes out to be 4.6123 times 10 to the 14th, and we can round that to two significant digits, 4.6 times 10 to the 14th hertz. Repeating for the violet light with a wavelength of 420 nm, or 4.20 times 10 to the negative 7th meters, we would get a frequency of 7.1381 times 10 to the 14th hertz. And we can round that to two significant digits, such that it becomes 7.1 times 10 to the 14th hertz.
Solution
- 4.6 x1014 Hz
- 7.1 x1014 Hz
Habbits of an Effective Problem Solver
- Read the problem carefully and develop a mental picture of the physical situation. If necessary, sketch a simple diagram of the physical situation to help you visualize it.
- Identify the known and unknown quantities and record in an organized manner, often times they can be recorded on the diagram itself. Equate given values to the symbols used to represent the corresponding quantity (e.g., \(\descriptive{v}{v,velocity} = \num{3e8}\unit{\meter\per\second}\), \(\descriptive{λ}{λ,wavelength} = 554 \unit{\nano\meter}\), \(\descriptive{f}{f,frequency} = \colorbox{gray}{Unknown}\)).
- Use physics formulas and conceptual reasoning to plot a strategy for solving for the unknown quantity.
- Identify the appropriate formula(s) to use.
- Perform substitutions and algebraic manipulations in order to solve for the unknown quantity.
Read About It!
Get more information on the topic of Light Waves and Colors at The Physics Classroom Tutorial.