Simple electronic energy level question

[Kibbel]

Homework Statement

A certain laser outputs pure green light (photon energy 2.5 eV) with power 500 milliwatts (0.5 watts). How many photons per second does this laser emit?

Homework Equations

not exactly sure, I know that Watts are equal to Jouls/sec
and that the electronic energy of a hydrogen atom is -13.6eV/N^2

The Attempt at a Solution

can someone run through this with me and give me a good explanation? do i convert .5 watts to eV and then divide that number by 2.5 eV?

3.121e+18(eV)/2.5 = 2.348e18?

 

[The CdePster]

Hiya! You're almost there m8 but one thing you got to remeber is that 1eV is equal to 1.6E-19 joules. so 2.5eV is what?? And then youre virtually there, because your right and watts are J/s and that thing is emitting 0.5 J/s.
Ha and just realized because i didnt check your first method is perfect however i don't know what you did because 3.121/2.5 does not equal 2.348! To avoid all the decimals though its MUCH easier to convert the 2.5eV to joules first. You get lovely round numbers then.

 

[Kibbel]

i don't understand this conceptually though, here is my new try with units, but i get a stupid answer at the end?

(1photon/2.5eV)*(.5*8e-20eV/s) = 3.2e-20 photons/second
but that can't possibley be correct

what did i flip or do wrong?

 

[The CdePster]

Hmm i don't understand your method at all ha! There should be no eV/s it should be in J/s.

OK here goes ill try and explain it, try and do it my way because i think its more intuitive :). Watts = the amount of joules evolved per second. First part to realize which you got. Secondly 1eV=1.6E-19 joules of energy. How many eV of energy does one photon have in this case?? 2.5eV! SO therefore the amount of energy in joules that one photon has in this case is 2.5*1.6E-19. That will be a MINISCULE amount like E-19. NOW this laser thing is pumping out 0.5 joules per second. How many photons is in that amount of energy?? Just divide 0.5 joules by that number you get for the energy of a photon. And youve got the number per second.

Now REMEMBER this because it is so cool and once you get good at it you can bomb through these questions like nothing. Look at the units of the thing your loking at. In this case we want s^-1 because its photons PER SECOND. We do not want joules so cancel out the joules while keeping s^-1. So like this watts are Js^-1, eV are in J we just did watts/eV which =(Js^-1)/J, oh and look we canceled out the J and are left with s^-1(aka per second). Trying to get to the right units at the end will almost always work. If you look at your attempt it ends up with J^-1 s^2 as its units, that aint going to give us the answer.

 

[rwisz]

I would approach this problem by first understanding the relationship between energy, power, and photons. Energy is measured in electron volts (eV) and power is measured in watts (W). A photon is a discrete unit of electromagnetic energy and its energy is determined by its frequency or wavelength. The energy of a photon can be calculated using the equation E = hf, where h is Planck's constant and f is the frequency of the photon. In this case, we are given the energy of the photon (2.5 eV) and the power of the laser (0.5 watts).

To find the number of photons emitted per second, we can use the equation P = nhf, where P is the power, n is the number of photons emitted per second, h is Planck's constant, and f is the frequency of the photon. Rearranging this equation, we get n = P/(hf).

Substituting the given values, we get n = 0.5/(2.5*1.602e-19), which gives us a value of 1.98e19 photons per second. This means that the laser is emitting almost 2 trillion photons per second.

It is important to note that the energy level of a hydrogen atom is not directly related to this problem and does not need to be considered in the solution. Also, converting watts to eV is not necessary as they are different units of measurement and cannot be directly converted. Instead, we use the equations and relationships between energy, power, and photons to solve the problem.