The compound eyes of bees and other insects are highly sensitive to light in the ultraviolet portion of the spectrum, specifically light with wavelengths between 300.0 nm and 400.0 nm. To what frequencies do these wavelengths correspond? (Assume that the speed of light to be 3.00 108 m/s.)
_________ Hz
_________ Hz
Oh, we're getting scientific now, huh? Alright, let me put on my geek glasses (which are just regular glasses, but they have tape in the middle).
To find the frequency of light, we can use the equation:
frequency = speed of light / wavelength
First, let's convert the wavelength from nanometers to meters:
300.0 nm = 300.0 x 10^-9 m
400.0 nm = 400.0 x 10^-9 m
Now, we can plug these values into the equation to find the frequencies:
frequency = (3.00 x 10^8 m/s) / (300.0 x 10^-9 m)
frequency = 1.00 x 10^15 Hz
frequency = (3.00 x 10^8 m/s) / (400.0 x 10^-9 m)
frequency = 7.50 x 10^14 Hz
So, the frequencies corresponding to these wavelengths are:
1.00 x 10^15 Hz
7.50 x 10^14 Hz
Now, don't ask me what the bees and other insects do with this information because I'm pretty sure they're just having a buzzing good time.
To convert wavelengths to frequencies, we can use the equation:
c = λv
Where:
c = speed of light (3.00 x 10^8 m/s)
λ = wavelength
v = frequency
To find the frequency, we can rearrange the equation to solve for v:
v = c / λ
For the ultraviolet light with a wavelength of 300.0 nm:
v = (3.00 x 10^8 m/s) / (300.0 x 10^-9 m)
v = 1.00 x 10^15 Hz
Therefore, the frequency is 1.00 x 10^15 Hz for a wavelength of 300.0 nm.
Similarly, for the ultraviolet light with a wavelength of 400.0 nm:
v = (3.00 x 10^8 m/s) / (400.0 x 10^-9 m)
v = 7.50 x 10^14 Hz
Therefore, the frequency is 7.50 x 10^14 Hz for a wavelength of 400.0 nm.
To find the frequencies corresponding to the given wavelengths, we can use the equation:
v = c / λ
where:
v = frequency (in Hz)
c = speed of light (in m/s)
λ = wavelength (in meters)
First, let's convert the given wavelengths from nm to meters:
300.0 nm = 300.0 × 10^-9 m
400.0 nm = 400.0 × 10^-9 m
Next, we can substitute the values into the equation to find the frequencies:
For 300.0 nm:
v1 = c / λ1
v1 = (3.00 × 10^8 m/s) / (300.0 × 10^-9 m)
v1 ≈ 1.00 × 10^15 Hz
For 400.0 nm:
v2 = c / λ2
v2 = (3.00 × 10^8 m/s) / (400.0 × 10^-9 m)
v2 ≈ 7.50 × 10^14 Hz
Therefore, the frequencies corresponding to the given wavelengths are:
1.00 × 10^15 Hz for 300.0 nm
7.50 × 10^14 Hz for 400.0 nm
1E15
and
7.5e14