Calculate the frequency of a wave that has an energy of 3.28x10^-19 J.

2 Answers

gsenviro's profile pic

gsenviro | College Teacher | (Level 1) Educator Emeritus

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The energy of a wave is related to its frequency by the following relationship: 

E = h x `nu` `<span class="AM"><br> </span>`

Where E denotes the energy of the wave, `nu`  is its frequency and h is the Planck's constant and has a value of 6.626 x 10^ (-34) J sec.

Substituting the value of energy (3.28 x 10^ (-19) J) and Planck's constant in the equation, we can solve for frequency as:

`nu`    = E/h = {3.28 x 10^-19}/{6.626 x 10^-34} 

= 4.95 x 10^14 Hz.

We can also calculate the wavelength of this wave, using the relationship between frequency and wavelength:

`nulambda` = c

Where, `nu`  is the frequency and `lambda`  is the wavelength of the wave. The constant c us the speed of light in vacuum and is equal to 3 x 10^8 m/s.

Hope this helps.

t-nez's profile pic

t-nez | High School Teacher | (Level 3) Associate Educator

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I assume that you are asking about electromagnetic radiation, which has a constant speed and a direct mathematical relationship between frequency and energy. That relationship is:

`E = h nu`

Where E = energy, `nu`  = frequency and h = Planck's constant which has a value of 

h = 6.623 x10^(-34) Joules x seconds

The energy per photon of radiation of this frequency is therefore:

E = 6.623 x 10^(-34) x 3.28 x 10^(-19) = 2.17 x 10^(-52)

A photon is a "quantum" unit of light energy. Planck's constant gives the energy per photon for a specific frequency. 

The frequency of electromagnetic radiation is inversely proportional to wavelength. So the higher the frequency, the higher the energy and the shorter the wavelength, the higher the energy.