What is the frequency of a green light with a wavelength of 520 nm?
[?] × 10
Hz
c = 3.0 x 108 m/s
Hint: Watch your units!
Be sure to enter both the coefficient and the exponent.
Coefficient (green)
Exponent (yellow)
provide the correct answer and 300 words explanation
To find the frequency (fff) of a green light with a given wavelength (λ\lambdaλ) of 520 nm, we use the wave equation:c=λfc = \lambda fc=λf
Where:
- ccc is the speed of light (3.0×108 m/s3.0 \times 10^8 \, \text{m/s}3.0×108m/s),
- λ\lambdaλ is the wavelength in meters,
- fff is the frequency in hertz (Hz).
Step 1: Convert the wavelength to meters
The given wavelength is 520 nm (nanometers). To convert nanometers to meters, we use the conversion factor:1 nm=1×10−9 m1 \, \text{nm} = 1 \times 10^{-9} \, \text{m}1nm=1×10−9m
Thus:520 nm=520×10−9 m=5.20×10−7 m520 \, \text{nm} = 520 \times 10^{-9} \, \text{m} = 5.20 \times 10^{-7} \, \text{m}520nm=520×10−9m=5.20×10−7m
Step 2: Rearrange the wave equation to solve for frequency
The wave equation is:c=λfc = \lambda fc=λf
Solving for fff:f=cλf = \frac{c}{\lambda}f=λc
Substitute the known values:f=3.0×108 m/s5.20×10−7 mf = \frac{3.0 \times 10^8 \, \text{m/s}}{5.20 \times 10^{-7} \, \text{m}}f=5.20×10−7m3.0×108m/s
Step 3: Calculate the frequency
Now, perform the calculation:f=3.0×1085.20×10−7=5.77×1014 Hzf = \frac{3.0 \times 10^8}{5.20 \times 10^{-7}} = 5.77 \times 10^{14} \, \text{Hz}f=5.20×10−73.0×108=5.77×1014Hz
Step 4: Express in scientific notation
The frequency of the green light is approximately:f=5.77×1014 Hzf = 5.77 \times 10^{14} \, \text{Hz}f=5.77×1014Hz
Explanation:
The frequency (fff) of electromagnetic waves is inversely proportional to the wavelength (λ\lambdaλ). Since green light has a wavelength of 520 nm, it falls within the visible spectrum, and we can see that the frequency is in the order of 101410^{14}1014 Hz. This frequency corresponds to light that oscillates 577 trillion times per second, which is typical for visible light in the green range.
In conclusion, the frequency of the green light with a wavelength of 520 nm is approximately 5.77×10145.77 \times 10^{14}5.77×1014 Hz.