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QuestionCalculate the number of photons in a laser pulse with energy 5.98 mJ5.98 \mathrm{~mJ} and wavelength 675 nm675 \mathrm{~nm}.

Studdy Solution

STEP 1

Assumptions1. The wavelength of the laser pulse is 675 nm675 \, nm . The energy of the laser pulse is 5.98 mJ5.98 \, mJ
3. We are using the equation =h⋅c/λ = h \cdot c / \lambda where $$ is the energy of one photon, $h$ is Planck's constant, $c$ is the speed of light, and $\lambda$ is the wavelength of the light4. Planck's constant $h =6.626 \times10^{-34} \, J \cdot s$
5. The speed of light $c =3.00 \times10^8 \, m/s$
6. The energy of the pulse is the sum of the energies of all the photons in the pulse

STEP 2

First, we need to find the energy of one photon. We can do this by using the equation =h⋅c/λ = h \cdot c / \lambda.
=h⋅cλ = \frac{h \cdot c}{\lambda}

STEP 3

Now, plug in the given values for Planck's constant, the speed of light, and the wavelength to calculate the energy of one photon.
=(6.626×10−34 J⋅s)⋅(3.00×108 m/s)675 nm = \frac{(6.626 \times10^{-34} \, J \cdot s) \cdot (3.00 \times10^8 \, m/s)}{675 \, nm}

STEP 4

Convert the wavelength from nanometers to meters.
675 nm=675×10−9 m675 \, nm =675 \times10^{-9} \, m=(6.626×10−34 J⋅s)⋅(3.00×108 m/s)675×10−9 m = \frac{(6.626 \times10^{-34} \, J \cdot s) \cdot (3.00 \times10^8 \, m/s)}{675 \times10^{-9} \, m}

STEP 5

Calculate the energy of one photon.
=(.626×10−34 J⋅s)⋅(3.00×108 m/s)675×10−9 m=2.95×10−19 J = \frac{(.626 \times10^{-34} \, J \cdot s) \cdot (3.00 \times10^8 \, m/s)}{675 \times10^{-9} \, m} =2.95 \times10^{-19} \, J

STEP 6

Now that we have the energy of one photon, we can find the number of photons in the laser pulse. This can be done by dividing the total energy of the pulse by the energy of one photon.
Number of photons=Total energyEnergy of one photonNumber\, of\, photons = \frac{Total\, energy}{Energy\, of\, one\, photon}

STEP 7

Convert the total energy from millijoules to joules.
5.98 mJ=5.98×10−3 J5.98 \, mJ =5.98 \times10^{-3} \, JNumber of photons=5.98×10−3 J2.95×10−19 JNumber\, of\, photons = \frac{5.98 \times10^{-3} \, J}{2.95 \times10^{-19} \, J}

STEP 8

Calculate the number of photons in the laser pulse.
Number of photons=5.98×10−3 J2.95×10−19 J=2.03×1016Number\, of\, photons = \frac{5.98 \times10^{-3} \, J}{2.95 \times10^{-19} \, J} =2.03 \times10^{16}The laser pulse contains 2.03×10162.03 \times10^{16} photons.

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