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  • Explain the relationship between the energy of a photon in joules or electron volts and its wavelength or frequency.
  • Calculate the number of photons per second emitted by a monochromatic source of specific wavelength and power.

Ionizing radiation

A photon is a quantum of EM radiation. Its energy is given by E = hf and is related to the frequency f and wavelength λ size 12{λ} {} of the radiation by

E = hf = hc λ (energy of a photon), size 12{E = ital "hf"= { { ital "hc"} over {λ} } } {}

where E size 12{E} {} is the energy of a single photon and c size 12{c} {} is the speed of light. When working with small systems, energy in eV is often useful. Note that Planck’s constant in these units is

h = 4 . 14 × 10 –15 eV s . size 12{h =" 4" "." "14 " times " 10" rSup { size 8{"–15"} } " eV " cdot " s"} {}

Since many wavelengths are stated in nanometers (nm), it is also useful to know that

hc = 1240 eV nm . size 12{ ital "hc" =" 1240 eV " cdot " nm"} {}

These will make many calculations a little easier.

All EM radiation is composed of photons. [link] shows various divisions of the EM spectrum plotted against wavelength, frequency, and photon energy. Previously in this book, photon characteristics were alluded to in the discussion of some of the characteristics of UV, x rays, and γ size 12{γ} {} rays, the first of which start with frequencies just above violet in the visible spectrum. It was noted that these types of EM radiation have characteristics much different than visible light. We can now see that such properties arise because photon energy is larger at high frequencies.

An electromagnetic spectrum is shown. Different types of radiation are indicated using double-sided arrows based on the ranges of their wavelength, energy, and frequency; the visible spectrum is shown, which is a very narrow band. The radio wave region is further segmented into A M radio, F M radio, and Microwaves bands.
The EM spectrum, showing major categories as a function of photon energy in eV, as well as wavelength and frequency. Certain characteristics of EM radiation are directly attributable to photon energy alone.
Representative energies for submicroscopic effects (order of magnitude only)
Rotational energies of molecules 10 5 size 12{"10" rSup { size 8{ - 5} } } {} eV
Vibrational energies of molecules 0.1 eV
Energy between outer electron shells in atoms 1 eV
Binding energy of a weakly bound molecule 1 eV
Energy of red light 2 eV
Binding energy of a tightly bound molecule 10 eV
Energy to ionize atom or molecule 10 to 1000 eV

Photons act as individual quanta and interact with individual electrons, atoms, molecules, and so on. The energy a photon carries is, thus, crucial to the effects it has. [link] lists representative submicroscopic energies in eV. When we compare photon energies from the EM spectrum in [link] with energies in the table, we can see how effects vary with the type of EM radiation.

Gamma rays , a form of nuclear and cosmic EM radiation, can have the highest frequencies and, hence, the highest photon energies in the EM spectrum. For example, a γ size 12{γ} {} -ray photon with f = 10 21 Hz size 12{f"= 10" rSup { size 8{"21"} } " Hz"} {} has an energy E = hf = 6.63 × 10 –13 J = 4 . 14 MeV. size 12{E = ital "hf""= 6" "." "63 " times " 10" rSup { size 8{"–13"} } " J"=4 "." "14"`"MeV"} {} This is sufficient energy to ionize thousands of atoms and molecules, since only 10 to 1000 eV are needed per ionization. In fact, γ size 12{γ} {} rays are one type of ionizing radiation    , as are x rays and UV, because they produce ionization in materials that absorb them. Because so much ionization can be produced, a single γ size 12{γ} {} -ray photon can cause significant damage to biological tissue, killing cells or damaging their ability to properly reproduce. When cell reproduction is disrupted, the result can be cancer, one of the known effects of exposure to ionizing radiation. Since cancer cells are rapidly reproducing, they are exceptionally sensitive to the disruption produced by ionizing radiation. This means that ionizing radiation has positive uses in cancer treatment as well as risks in producing cancer.

Questions & Answers

A golfer on a fairway is 70 m away from the green, which sits below the level of the fairway by 20 m. If the golfer hits the ball at an angle of 40° with an initial speed of 20 m/s, how close to the green does she come?
Aislinn Reply
cm
tijani
what is titration
John Reply
what is physics
Siyaka Reply
A mouse of mass 200 g falls 100 m down a vertical mine shaft and lands at the bottom with a speed of 8.0 m/s. During its fall, how much work is done on the mouse by air resistance
Jude Reply
Can you compute that for me. Ty
Jude
what is the dimension formula of energy?
David Reply
what is viscosity?
David
what is inorganic
emma Reply
what is chemistry
Youesf Reply
what is inorganic
emma
Chemistry is a branch of science that deals with the study of matter,it composition,it structure and the changes it undergoes
Adjei
please, I'm a physics student and I need help in physics
Adjanou
chemistry could also be understood like the sexual attraction/repulsion of the male and female elements. the reaction varies depending on the energy differences of each given gender. + masculine -female.
Pedro
A ball is thrown straight up.it passes a 2.0m high window 7.50 m off the ground on it path up and takes 1.30 s to go past the window.what was the ball initial velocity
Krampah Reply
2. A sled plus passenger with total mass 50 kg is pulled 20 m across the snow (0.20) at constant velocity by a force directed 25° above the horizontal. Calculate (a) the work of the applied force, (b) the work of friction, and (c) the total work.
Sahid Reply
you have been hired as an espert witness in a court case involving an automobile accident. the accident involved car A of mass 1500kg which crashed into stationary car B of mass 1100kg. the driver of car A applied his brakes 15 m before he skidded and crashed into car B. after the collision, car A s
Samuel Reply
can someone explain to me, an ignorant high school student, why the trend of the graph doesn't follow the fact that the higher frequency a sound wave is, the more power it is, hence, making me think the phons output would follow this general trend?
Joseph Reply
Nevermind i just realied that the graph is the phons output for a person with normal hearing and not just the phons output of the sound waves power, I should read the entire thing next time
Joseph
Follow up question, does anyone know where I can find a graph that accuretly depicts the actual relative "power" output of sound over its frequency instead of just humans hearing
Joseph
"Generation of electrical energy from sound energy | IEEE Conference Publication | IEEE Xplore" ***ieeexplore.ieee.org/document/7150687?reload=true
Ryan
what's motion
Maurice Reply
what are the types of wave
Maurice
answer
Magreth
progressive wave
Magreth
hello friend how are you
Muhammad Reply
fine, how about you?
Mohammed
hi
Mujahid
A string is 3.00 m long with a mass of 5.00 g. The string is held taut with a tension of 500.00 N applied to the string. A pulse is sent down the string. How long does it take the pulse to travel the 3.00 m of the string?
yasuo Reply
Who can show me the full solution in this problem?
Reofrir Reply
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Source:  OpenStax, College physics. OpenStax CNX. Jul 27, 2015 Download for free at http://legacy.cnx.org/content/col11406/1.9
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