# Number of photons for multi-photon laser ionization

• Lion.P
In summary, to find the number of photons needed for multi-photon ionization of a single nitrogen molecule, you would first calculate the energy of a single photon from the frequency of the laser beam. Then, you would divide the ionization energy per mole by the energy of a single photon and then by Avogadro's number to get the number of photons per molecule.
Lion.P

## Homework Statement

The ionization potential of a nitrogen molecule is 15.5 eV.

How many photons from a beam of a 1054 nm high power laser must be absorbed by a nitrogen molecule simultaneously to cause multi-photon ionization?

None were given.

## The Attempt at a Solution

I wasn't too sure where to start

First I used E = hc/λ to find the energy of the beam:

E = (6.62608E-34 Js)(2.998E10 m/s)/(1054 nm)(1m/1E9nm) = 1.885 E-17 J

Next I converted the ionization potential to J/mol:

15.5 eV/atom * (1 kJ/mol)/(0.010364 eV/atom) * (1000 J/kJ) = 1.4956E6 J/mol

I tried dividing the two energies out and dividing by Avogadro number but that gives me a very small amount of photons & the units do not include photons. If anyone has an idea of where to look next or a hint I'd appreciate it.

Thanks

for your question! It looks like you're on the right track with your calculations. However, there are a few things you could consider to get a more accurate answer.

First, it's important to note that the ionization potential you have given is for a single nitrogen molecule, not a mole of nitrogen molecules. So, your calculation for the ionization energy per mole should actually be:

15.5 eV/atom * (1 kJ/mol)/(0.010364 eV/atom) * (1000 J/kJ) = 1.4956E6 J/mol

Also, keep in mind that the energy of a single photon is given by Planck's constant (h) times the frequency (ν), not the wavelength (λ). So, you should use the frequency of the laser beam (ν) to calculate the energy of a single photon:

E = h*ν = (6.62608E-34 Js)(2.998E10 m/s)/(1054 nm)(1m/1E9nm) = 5.945E-19 J

Now, to find the number of photons needed for multi-photon ionization, you can divide the ionization energy per mole by the energy of a single photon:

(1.4956E6 J/mol) / (5.945E-19 J/photon) = 2.517E24 photons/mol

Keep in mind that this is the number of photons needed for multi-photon ionization of a mole of nitrogen molecules. To find the number of photons needed for a single nitrogen molecule, you would need to divide by Avogadro's number (6.022E23 molecules/mol):

(2.517E24 photons/mol)/(6.022E23 molecules/mol) = 4.182 photons/molecule

So, to answer the original question, you would need approximately 4 photons from the high power laser beam to cause multi-photon ionization of a single nitrogen molecule.

## 1. What is multi-photon laser ionization?

Multi-photon laser ionization is a process in which multiple photons are used to ionize an atom or molecule. This is in contrast to single-photon ionization, where only one photon is used to remove an electron.

## 2. How many photons are required for multi-photon laser ionization?

The number of photons required for multi-photon laser ionization depends on the energy of the photons and the ionization energy of the atom or molecule being ionized. Generally, at least two or more photons are needed for multi-photon ionization.

## 3. How does the number of photons affect the efficiency of multi-photon laser ionization?

The efficiency of multi-photon laser ionization increases as the number of photons increases. This is because a higher number of photons means a higher probability of absorption and ionization of the atom or molecule.

## 4. What factors can affect the number of photons required for multi-photon laser ionization?

The energy of the photons, the ionization energy of the atom or molecule, and the intensity of the laser beam are all factors that can affect the number of photons required for multi-photon ionization. Higher energy photons and higher laser beam intensity can reduce the number of photons needed for ionization.

## 5. What are the applications of multi-photon laser ionization?

Multi-photon laser ionization has various applications in fields such as analytical chemistry, materials science, and biomedical research. It is commonly used for surface analysis, imaging techniques, and selective ionization of specific molecules for analysis.

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