To find the frequency of blue light given its wavelength, we can use the relationship between the speed of light ([tex]\( c \)[/tex]), wavelength ([tex]\( \lambda \)[/tex]), and frequency ([tex]\( f \)[/tex]). The formula is:
[tex]\[ f = \frac{c}{\lambda} \][/tex]
Here’s the given data:
- Wavelength ([tex]\( \lambda \)[/tex]) = [tex]\( 4.83 \times 10^{-7} \)[/tex] meters
- Speed of light ([tex]\( c \)[/tex]) = [tex]\( 3.0 \times 10^8 \)[/tex] meters per second
Now, let's substitute the given values into the formula.
1. We have:
[tex]\[ f = \frac{3.0 \times 10^8 \, \text{m/s}}{4.83 \times 10^{-7} \, \text{m}} \][/tex]
2. Perform the division:
[tex]\[ f \approx \frac{3.0 \times 10^8}{4.83 \times 10^{-7}} \][/tex]
3. To express the result in scientific notation, let's break the calculation into parts.
- First, divide the coefficients (numbers in front):
[tex]\[
\frac{3.0}{4.83} \approx 0.6219 \, (\text{approximate value})
\][/tex]
- Then, handle the power of ten:
[tex]\[
\frac{10^8}{10^{-7}} = 10^{8 - (-7)} = 10^{15}
\][/tex]
4. Combine both results:
[tex]\[ f \approx 0.6219 \times 10^{15} \, \text{Hz} \][/tex]
Now, to match the scientific notation format:
[tex]\[ f \approx 6.21 \times 10^{14} \, \text{Hz} \][/tex]
So, the frequency of the blue light with a wavelength of [tex]\( 4.83 \times 10^{-7} \)[/tex] meters is approximately [tex]\( 6.21 \times 10^{14} \)[/tex] Hz.
