A laser pulse with wavelength 540 nm contains 4.40 Mj of energy. How many photons are in the laser pulse?
First calculate the energy of one photon.
E = hc/lambda
Then knowing the total energy you can calculate the number of photons.
To find the number of photons in the laser pulse, we can use the formula:
E = n * h * c / λ
where:
E = energy of the laser pulse
n = number of photons
h = Planck's constant (6.626 x 10^-34 J·s)
c = speed of light (3.00 x 10^8 m/s)
λ = wavelength of the laser pulse
First, let's convert the energy from megajoules to joules:
4.40 Mj = 4.40 x 10^6 J
Now, let's substitute the values into the formula and solve for n:
4.40 x 10^6 J = n * (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (540 x 10^-9 m)
Simplifying the expression:
4.40 x 10^6 J = n * (6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s) / (540 x 10^-9 m)
n = (4.40 x 10^6 J) * (540 x 10^-9 m) / [(6.626 x 10^-34 J·s) * (3.00 x 10^8 m/s)]
Evaluating the expression:
n ≈ 5.5556 x 10^21 photons
Therefore, there are approximately 5.5556 x 10^21 photons in the laser pulse.
To calculate the number of photons in a laser pulse, we need to know the energy of each photon. We can use the equation E = hc/λ, where E is the energy of the photon, h is Planck's constant (6.626 x 10^-34 J s), c is the speed of light (3.00 x 10^8 m/s), and λ is the wavelength of the photon.
First, let's convert the energy of the laser pulse into joules. 1 megajoule (Mj) is equal to 1 million joules. So, 4.40 Mj can be written as 4.40 x 10^6 J.
Now, we can rearrange the equation to solve for the energy of each photon:
E = hc/λ
Let's substitute the known values:
4.40 x 10^6 J = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s) / λ
Now, we can solve for λ by rearranging the equation:
λ = (6.626 x 10^-34 J s)(3.00 x 10^8 m/s) / (4.40 x 10^6 J)
Calculating λ, we find:
λ ≈ 4.51 x 10^-7 m
Now, we can calculate the number of photons using the equation:
Number of photons = Total energy / Energy per photon
Number of photons = 4.40 x 10^6 J / (6.626 x 10^-34 J s)(3.00 x 10^8 m/s) / 4.51 x 10^-7 m
Calculating the number of photons, we find:
Number of photons ≈ 4.41 x 10^24 photons
Therefore, there are approximately 4.41 x 10^24 photons in the laser pulse with a wavelength of 540 nm and an energy of 4.40 Mj.