Find the frequency f in terahertz of visible light with a wavelength of 535 nm in vacuum. f= THz
What is the wavelength in centimeters of electromagnetic microwave radiation whose frequency is 7.25 GHz?
The correct answer and explanation is :
To calculate the frequency ( f ) of visible light with a wavelength of 535 nm, we can use the formula that relates the speed of light (( c )), frequency (( f )), and wavelength (( \lambda )):
[
c = f \lambda
]
Where:
- ( c ) is the speed of light, approximately ( 3 \times 10^8 \, \text{m/s} ).
- ( f ) is the frequency in hertz (Hz).
- ( \lambda ) is the wavelength in meters (m).
First, we convert the wavelength from nanometers (nm) to meters (m):
[
\lambda = 535 \, \text{nm} = 535 \times 10^{-9} \, \text{m}
]
Now, solve for the frequency ( f ):
[
f = \frac{c}{\lambda} = \frac{3 \times 10^8 \, \text{m/s}}{535 \times 10^{-9} \, \text{m}} = 5.61 \times 10^{14} \, \text{Hz}
]
Since ( 1 \, \text{THz} = 10^{12} \, \text{Hz} ), the frequency in terahertz is:
[
f = \frac{5.61 \times 10^{14}}{10^{12}} = 561 \, \text{THz}
]
So, the frequency of visible light with a wavelength of 535 nm is 561 THz.
Now, let’s calculate the wavelength of electromagnetic microwave radiation with a frequency of 7.25 GHz.
First, recall the formula for the speed of light:
[
c = f \lambda
]
Where:
- ( c = 3 \times 10^8 \, \text{m/s} ) is the speed of light.
- ( f = 7.25 \, \text{GHz} = 7.25 \times 10^9 \, \text{Hz} ) is the frequency.
We want to find the wavelength ( \lambda ), so rearrange the formula to solve for ( \lambda ):
[
\lambda = \frac{c}{f}
]
Substitute the known values:
[
\lambda = \frac{3 \times 10^8 \, \text{m/s}}{7.25 \times 10^9 \, \text{Hz}} = 0.04138 \, \text{m}
]
Finally, convert the wavelength to centimeters (1 meter = 100 cm):
[
\lambda = 0.04138 \, \text{m} \times 100 = 4.138 \, \text{cm}
]
So, the wavelength of electromagnetic microwave radiation with a frequency of 7.25 GHz is 4.138 cm.
Summary:
- The frequency of visible light with a wavelength of 535 nm is 561 THz.
- The wavelength of electromagnetic microwave radiation with a frequency of 7.25 GHz is 4.138 cm.
Here is an educational diagram illustrating the relationship between frequency and wavelength for visible light and microwave radiation. It shows the wavelength and frequency for each type of wave and highlights the connection between them.