Answer:
a) Remember the relationship:
v = f*λ
where:
v = velocity of the wave, remember that for an electromagnetic wave, this always is equal to the speed of light, then:
v = c = 3*10^8 m/s
f is the frequency of the wave
λ is the wavelength.
So if we want to compute the frequency, we have the equation:
f = c/λ
then:
We know that UVA has the range from 320 nm to 400nm, converting these to meters we hav:
1nm = 1m*10^(-9)
then:
320mm = (320*10^(-9)) m = 0.00000032 m
400nm = (400*10^(-9)) m = 0.00000040 m
Replacing these in our equation we can find that the range of frequencies is:
f = (3*10^8 m/s)/( 0.00000032 m) = 9.375*10^(14) Hz
f = (3*10^8 m/s)/( 0.00000040 m) = 7.5*10^(14) Hz
Then the range of frequencies is:
( 7.5*10^(14) Hz to 9.375*10^(14) Hz)
Similar for the case of UVB:
the wavelengths are:
280 nm to 320 nm
Rewriting these in meters we get:
280nm = 280*10^(-9) m = 0.00000028m
320nm = 320*10^(-9) m = 0.00000032 m
Then the frequencies are:
f = (3*10^8 m/s)/( 0.00000032 m) = 9.375*10^(14) Hz
f = (3*10^8 m/s)/( 0.00000028 m) = 1.07*10^(15) Hz
The range of frequencies for UVB is:
(9.375*10^(14) Hz to 1.07*10^(15) Hz)
B) We want to know the range of wavenumbers for both types of waves.
The wave number is calculated as:
1/λ
Which represents the number of waves in a given unit of length.
Then the range for UVA will be:
1/320nm = 0.0031 nm^-1
1/400nm = 0.0025 nm^-1
Then the range is:
( 0.0025 nm^-1, 0.0031 nm^-1)
And for the case of UVB we will have:
1/320 nm = 0.0031 nm^-1
1/280 nm = 0.0036 nm^-1
Then the range is:
(0.0031 nm^-1, 0.0036 nm^-1)
