Value: Calculate the frequency of blue light that has a wavelength of 500 nm: 1.66 X 10-15 , 1.66 x 1014 s-1 6.0 x 1014 81 6.0 x 10-14 s-1 Check Answer
The Correct Answer and Explanation is:
To calculate the frequency of blue light with a wavelength of 500 nm, we use the equation from wave physics: f=cλf = \frac{c}{\lambda}
Where:
- ff = frequency (in hertz or s⁻¹)
- cc = speed of light = 3.00×1083.00 \times 10^8 m/s
- λ\lambda = wavelength (in meters)
Step-by-Step Calculation:
Given:
- λ=500\lambda = 500 nm = 500×10−9500 \times 10^{-9} m = 5.00×10−75.00 \times 10^{-7} m
- c=3.00×108c = 3.00 \times 10^8 m/s
Now, plug into the formula: f=3.00×108 m/s5.00×10−7 m=6.00×1014 Hz (or s−1)f = \frac{3.00 \times 10^8 \text{ m/s}}{5.00 \times 10^{-7} \text{ m}} = 6.00 \times 10^{14} \text{ Hz (or s}^{-1}\text{)}
✅ Correct Answer: 6.00×1014 s−16.00 \times 10^{14} \, \text{s}^{-1}
Explanatio
Light behaves both as a particle and a wave, and when considering its wave nature, we use concepts such as frequency and wavelength. Frequency (ff) refers to how many wave crests pass a point in one second, while wavelength (λ\lambda) is the distance between two consecutive crests. The product of frequency and wavelength equals the speed of light in a vacuum (cc): c=fλc = f \lambda
To find the frequency, we rearrange the formula: f=cλf = \frac{c}{\lambda}
In this problem, we are given the wavelength of blue light as 500 nanometers (nm), which needs to be converted to meters because the speed of light is in meters per second. Since 1 nm=10−9 m1 \, \text{nm} = 10^{-9} \, \text{m}, we convert 500 nm to: 500 nm=5.00×10−7 m500 \, \text{nm} = 5.00 \times 10^{-7} \, \text{m}
Substituting the values into the equation: f=3.00×1085.00×10−7=6.00×1014 s−1f = \frac{3.00 \times 10^8}{5.00 \times 10^{-7}} = 6.00 \times 10^{14} \, \text{s}^{-1}
This result means that a blue light wave with a wavelength of 500 nm oscillates 600 trillion times per second. This frequency falls within the visible light spectrum and corresponds to blue light. Incorrect options like 1.66×10−151.66 \times 10^{-15} or 1.66×10141.66 \times 10^{14} either reflect a misunderstanding of unit conversions or incorrect application of the wave equation. Thus, 6.00×1014 s−16.00 \times 10^{14} \, \text{s}^{-1} is the correct and scientifically supported answer.
