What is the frequency of radiation if its wavelength is 5.80 x 10^-7 m?

Understand the Problem

The question is asking us to calculate the frequency of radiation given its wavelength using the formula that relates wavelength and frequency, which is c = λf, where c is the speed of light, λ is the wavelength, and f is the frequency.

Answer

$6 \times 10^{14} \, \text{Hz}$

Steps to Solve

Identify the known values
We know the speed of light, ( c ), which is approximately ( 3 \times 10^8 ) meters per second (m/s). We also have the wavelength, ( \lambda ), that we need to use in our calculations.
Rearrange the formula
To find the frequency ( f ), we can rearrange the equation ( c = \lambda f ) to solve for ( f ):

$$ f = \frac{c}{\lambda} $$
Substitute known values
Substitute the known values into the rearranged formula. For example, if the wavelength ( \lambda ) is given as ( 500 ) nm (nanometers), we need to convert that into meters: $$ 500 , \text{nm} = 500 \times 10^{-9} , \text{m} $$

Now plug ( c ) and ( \lambda ) into the equation for ( f ):
$$ f = \frac{3 \times 10^8}{500 \times 10^{-9}} $$
Calculate the frequency
Now, perform the calculation to find ( f ): $$ f = \frac{3 \times 10^8}{500 \times 10^{-9}} = \frac{3 \times 10^8}{5 \times 10^{-7}} = 6 \times 10^{14} , \text{Hz} $$

The frequency of radiation given a wavelength of ( 500 ) nm is ( 6 \times 10^{14} , \text{Hz} ).

More Information

The frequency ( 6 \times 10^{14} , \text{Hz} ) corresponds to light in the visible spectrum, particularly green light. The relationship between wavelength and frequency is fundamental in understanding electromagnetic radiation and helps in various applications in science and technology.

Tips

Forgetting to convert the wavelength from nanometers to meters can lead to incorrect frequency calculations. Always ensure you're using consistent units before substituting in the formula.

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