Question

No of photons when wavelength and energy produce is given

Answer 1

Every photon has a characteristic energy associated with it. The energy of a photon is dependent on its frequency. The way I would solve this is to convert the wavelength, 679 nm, to a frequency and then find the energy. After we know the energy of a single photon, we can find out how many it takes to get the total energy of the pulse (0.528 J).

Some useful equations:

λν = c

Wavelength, λ (lambda), times frequency, ν (nu), equals the speed of light.

c = 3.0 x 108 m/s.

E = hν

Energy of a single photon is the product of Planck's constant, h, and the frequency, ν. h = 6.63 x 10-34 J•s.

I prefer to manipulate the equations before plugging in our known values.

We have a wavelength as a known, so let's solve for the energy of a single photon at that wavelength:

λν = c

ν = c/λ

Plug this into the other equation:

E = hν

E = hc/λ

Now we can plug in our two constants (h and c, they never change) and our known (λ = 679 nm = 679 x 10-9 m) and find the energy of a single photon. Make sure you use the value of the wavelength in meters (679 x 10-9 m).

E = 2.93 x 10-19

Let's check our units:

h is in J•s (energy • time). c is in m/s (distance/time). Wavelength is in m (after we converted from nm).

So our final units should be: (J•s•m/s)/m = (J•s•m/s)/m = (J•m)/m = J

Good, that is what we wanted.

Each photon of light at 679 nm is 2.93 x 10-19 J of energy. The whole pulse is 0.528 J. It is a simple matter of division to get:

0.528 J / 2.93 x 10-19 J = 1.8 x 1018 photons

We divided the energy of the whole pulse by the energy per photon to get the number of photons.