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Photon Energy Calculator + Online Solver With Free Steps


The Photon Energy Calculator calculates the energy of photons by using the frequency of that photon (in the electromagnetic spectrum)  and the energy equation “E = hv.

Furthermore, this calculator gives the details of the energy equation alongside the frequency range, where the photon lies.

The calculator does not support calculations properly in the case where the frequency units, Hertz, are not mentioned besides the expected value. Hence, the units are necessary for the calculator to work correctly.

Moreover, the calculator supports engineering prefixes such as Kilo-, Mega-, and Giga- in the form of K, M, and G before the unit. It helps in writing large values in short form.

What Is the Photon Energy Calculator?

The Photon Energy Calculator is an online tool that calculates the photon’s energy by multiplying Planck’s Constant (h) with the radiation frequency of the photon. Additionally, it provides steps and details of the governing equation used to find the Photon Energy. 

The calculator consists of a single-line text box labeled “frequency,” where you can enter the frequency of the desired photon. It is necessary that the units,  hertz, are mentioned after the frequency value is entered for the calculator to work correctly.

How To Use the Photon Energy Calculator?

You can utilize the Photon Energy Calculator by simply entering the frequency range of the photon in the text box and pressing the “submit” button. A pop-up window will show the detailed results. 

The guidelines for the calculator’s usage are below.

Step 1

Enter the frequency value of the desired photon for which you want to calculate the energy.

Step 2

Ensure that the frequency is entered correctly with unit hertz (Hz) after entering it. Furthermore, ensure the appropriate usage of the prefix in the frequency value.

Step 3

Press the “Submit” button to get the results. 

Results

A pop-up window appears showing the detailed results in the sections explained below: 

  • Input Information: This section shows the input frequency value with the unit prefix and the unit, hertz (Hz), besides it.
  • Result: This section shows the result, that is, the photon energy value, in the form of 3 unit forms: Joules (J), Electron-Volts (eV), and British Thermal Units (BTU). All the energy values are in standard form.
  • Equation: This section elaborates on the equation used to calculate the Photon energy “E = hν” and further explains each variable in different rows.
  • Electromagnetic frequency range: This section tells the frequency range in the electromagnetic spectrum to which the photon belongs according to its frequency value.

How Does the Photon Energy Calculator Work?

The Photon Energy Calculator works by using the energy equation to compute the total energy emitted or absorbed by the photon when an atom goes down or up the energy level. To further understand the concepts of photons and energy levels, we will elaborate on the definition of these terms. 

Definition

A photon is a small particle made up of electromagnetic radiation waves. They are just electric fields flowing across space, as demonstrated by Maxwell. Photons have no charge and no rest mass, thus moving at the speed of light. Photons are emitted by the action of charged particles, but they can also be emitted by other processes, such as radioactive decay.

The energy carried by a single photon is called photon energy. The quantity of energy is related to the electromagnetic frequency of the photon and consequently inversely proportional to the wavelength. The higher the frequency of a photon, the greater its energy. The longer the wavelength of a photon, the lower its energy.

The energy absorbed by an atom to move from a ground state energy level to an upper energy level is equal to the photon’s energy that causes it to jump an energy level. This energy is determined using the general formula: 

\[ E = \frac{hc}{\lambda}\]

Where E is the energy of a photon in Joules, h is Planck’s constant, c is the speed of light in a vacuum, and λ is the photon’s wavelength

Generally, this value is in electron-volts (eV) that can be converted by dividing the energy in joules by 1 eV = 1.6 x 10^-19 J.

Solved Examples

Example 1

When a mercury atom falls to a lower energy level, a photon of frequency 5.48 x 10^14 Hz is released. Determine the energy emitted during the process. 

Solution

Given is the frequency (ν) = 5.48 x 10^14 Hz. Using the general photon energy equation, we can determine the energy as follows:

E = h$\nu$

E = (6.63 x 10$^{-34}$) x ( 5.48 x 10$^{14}$)

E = 3.63 x 10^{-19} J 

Since we represent this energy in the electron-volts unit, we need to divide “E” with 1 eV = 1.6 x 10^-19.

E = $\dfrac{3.63 \times 10^{-19} }{1.6 \times 10^{-19} }$

E = 2.26 eV

Hence, the Energy, E, is equal to 2.26 eV. 

Example 2

A mercury atom moves to an upper level when a photon of wavelength 2.29 x 10^-7 meters strikes it. Calculate the energy absorbed by this mercury atom. 

Solution

In this example, we first have to find the frequency of the photon that strikes the mercury atom. We can find it by dividing the speed of light, c = 3 x 10^18, by the wavelength 

\[ \text{frequency }(\nu) = \frac{\text{Speed of light (c)}}{\text{wavelength } (\lambda)} \]

\[\nu = \frac{3 \times 10^{18}}{2.29 \times 10^7} \]

\[ \nu = 1.31 \times 10^{11} \]

Now, using the frequency we calculated and the general photon energy equation, we can determine the energy as follows:

E = h$\nu$

E = (6.63 x 10$^{-34}$) x ( 1.31 x 10$^{11}$) 

E = 8.68 x 10$^{-23}$ J

Since we represent this energy in the electron-volts unit, we need to divide “E” with 1 eV = 1.6 x 10-19.

E = $\dfrac{8.68 \times 10^{-23} }{1.6 \times 10^{-19} }$ 

E = 5.42 x 10$^{-4}$ eV

Hence, the Energy, E, is 5.42 x 10-4 eV. 

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