With this photon energy calculator, you can explore the relationship between the wavelength and frequency of the photon and its energy. Read the text below to find out how to calculate the energy of a photon and what is Planck's equation.
The light seems to us to have a wavy character. It diffracts, interferes, and refracts. However, at a microscopic level, it is carried by a minuscule quantum of energy called the photon. The energy of a photon depends solely on its wavelength or frequency. Because light travels, well, at the speed of light, we can use either frequency or wavelength to describe it. You can check the wavelength calculator to explore the relationship between the wavelength and frequency.
Coming back to photons, what is their energy? The energy of a single photon is a tiny number given by Planck's equation. Planck's equation relates the frequency of a photon to its energy through a Planck constant hhh equal to:
h=6.6261×10−34 J⋅s\small h = 6.6261 \times 10^{-34}\ \text{J}\cdot\text{s}h=6.6261×10−34 J⋅s
The Planck constant is in the units (energy)·(time), and you can think of it as a conversion factor from energies to frequencies.
Planck's photo energy equation is:
E=hcλ=hf\small E = \frac{hc}{\lambda} = hfE=λhc=hf
where:
- EEE – Energy of a photon;
- hhh – Planck constant;
- ccc – Speed of light;
- λλλ – Wavelength of a photon; and
- fff – Frequency of a photon.
This equation gives us the energy of a single, indivisible quanta of light, and we can think of light as a collection of particles. The opposite is also true. We can think about ordinary particles, like electrons, as waves. Check De Broglie wavelength calculator to learn more about this concept.
The energy of a single photon is a small number because the Planck constant is ridiculously tiny. The energy of a single photon of green light of a wavelength of 520 nm has an energy of 2.38 eV. You can use the photon energy calculator to explore further the relationship between the photon energy and its frequency or wavelength.
The answer is #3.54xx"10"^(-19)" J"#.
The equation for determining the energy of a photon of electromagnetic radiation is #E=hnu#, where E is energy in Joules, h is Planck's constant, #6.626 xx"10"^(-34)"J"*"s"#, and #nu# (pronounced "noo") is the frequency.
You have been given the wavelength #lambda# (pronounced lambda) in nanometers, but not the frequency.
Fortunately, a relationship between wavelength, frequency, and the speed of light, #c# exists, such that #c=lambda*nu#. To determine the frequency from the wavelength, divide #c# by #lambda#:
#nu=(c)/(lambda)#
We can substitute #(c)/(lambda)# for #nu# in the first equation, so that:
#E=h*(c)/(lambda)#
The speed of light, #c#, is usually given as #3.00xx10^8"m/s"# rounded to three significant figures. So the wavelength must first be converted from nm to m. #1 "m"=1xx10^9 "nm"#. To convert nm to m, do the following calculation:
#562 color(red)cancel(color(black)( "nm"))xx(1"m")/(1xx10^9 color(red)cancel(color(black)("nm")))="0.000000562m"=5.62xx"10"^(-7) "m"#
Now we're ready to determine the amount of energy in Joules in one photon of green light with the wavelength #"562 nm"#.
#E=hnu=h*(c)/(lambda)#
Substitute the known values into the equation and solve.
#6.626xx"10"^(-34)"J"*color(red)cancel(color(black)("s"))xx(3.00xx"10"^8color(red)cancel(color(black)("m"))/color(red)cancel(color(black)("s")))/(5.62xx"10"^(-7)color(red)cancel(color(black)("m")))=3.54xx"10"^(-19)" J"#
Green light has a frequency of about 6.00 x 10^14 s-1 . What is the energy of a photon of green light?
4 sigfig
E=J
Hospital X-ray generators emit X rays with wavelength of about 15.0 nanometers (), where 1 nm = 10^9 m. What is the energy of a photon in an X ray?
Express answer in joules.
Concepts and reason The concept used to solve this problem is based on the energy of a photon.
The energy of the photons is calculated using the Planck’s law when their frequency is known. The energy can also be calculated when only the wavelength is known. The wave equation is used to first calculate the frequency and then it is substituted in the Planck’s equation.
Fundamentals The energy of a photon can be calculated using the Planck’s equation:
Answer:
Explanation:
The frequency of the photon is known. Using this, the energy of the photon is calculated by Planck’s equation.
Since the answer has to be reported in 4 significant figures, therefore the energy of a photon of green light is
Explanation: