A particular form of electromagnetic radiation has a frequency of 5.42x10^15 Hz. What is the wavelength is nanometers? meters? reply in scientific notation.
c = frequency x wavelength.
c = 3E8 m/s. Wavelength will be in meters. Convert to nm by multiplying by 1E9.
what is the energy in joules of one quantum of this radiation? reply in scientific notation.
To find the wavelength of electromagnetic radiation, you can use the formula:
wavelength = speed of light / frequency
The speed of light is approximately 3.00 x 10^8 meters per second (m/s).
Given the frequency, which is 5.42 x 10^15 Hz, you can now calculate the wavelength using the formula mentioned above.
1. Convert the frequency to meters per second (m/s):
5.42 x 10^15 Hz = 5.42 x 10^15 s^-1
2. Plug the values into the wavelength formula:
wavelength = (3.00 x 10^8 m/s) / (5.42 x 10^15 s^-1)
To simplify the calculation, divide the numerator and denominator by 10^8:
wavelength = 3.00 / 5.42 x 10^(8 - 15) m
Since the exponent in the denominator is negative, move it to the numerator and change the sign to positive:
wavelength = 3.00 / 5.42 x 10^(15 - 8) m
Now, calculate the value in the brackets:
wavelength = 3.00 / 5.42 x 10^7 m
Finally, convert the wavelength to nanometers by multiplying it by 10^9 (since 1 meter = 10^9 nanometers):
wavelength = (3.00 / 5.42 x 10^7) x 10^9 nm
Simplify the expression inside the brackets:
wavelength = 0.553 x 10^9 nm
This value can be written in scientific notation as:
wavelength = 5.53 x 10^8 nm (rounded to two significant figures)
So, the wavelength of the electromagnetic radiation is approximately 5.53 x 10^8 nanometers (nm) and 0.553 meters (m).