One type of sunburn occurs on exposure to UV light wavelength in the vicinity of 325nm.
How many photons are in 1.00 mJ burst of this radiation?
E = hc/lambda
h = Planck's constant = 6.626 x 10^-34 J*s.
c is speed of light = 3 x 10^8 m/s.
lambda is 325 nm. Put this in meters.
E = Joules for 1 photon = xx.
Then (xxJ/1 photon) = (1.00 mJ/?)
Solve for ?. Be sure and put 1.00 mJ in as J.
1.64*10^15
To calculate the number of photons in a 1.00 mJ burst of radiation, we can use the following formula:
Energy (E) = Number of photons (N) * Energy per photon (Eph)
First, we need to convert the energy of 1.00 mJ to joules:
1.00 mJ = 1.00 x 10^-3 J
The energy per photon can be calculated using the formula:
Eph = hc / λ
Where:
h = Planck's constant = 6.626 x 10^-34 J·s
c = speed of light = 3.00 x 10^8 m/s
λ = wavelength = 325 nm = 325 x 10^-9 m
Now let's calculate the energy per photon (Eph):
Eph = (6.626 x 10^-34 J·s x 3.00 x 10^8 m/s) / (325 x 10^-9 m)
= 6.459 x 10^-19 J
Next, we can substitute the values into the formula:
1.00 x 10^-3 J = N * (6.459 x 10^-19 J)
Now we can solve for the number of photons (N):
N = (1.00 x 10^-3 J) / (6.459 x 10^-19 J)
= 1.55 x 10^15 photons
Therefore, there are approximately 1.55 x 10^15 photons in a 1.00 mJ burst of radiation with a wavelength of 325 nm.
To determine the number of photons in a given burst of radiation, you need to use the relationship between energy (in joules), the speed of light, and Planck's constant.
The formula you need to use is:
Energy = Number of Photons × (Planck's constant × Speed of light) / Wavelength
In this case, the energy is given as 1.00 mJ, which needs to be converted into joules. Since 1 mJ = 0.001 J, the energy is equal to 0.001 J.
The wavelength is given as 325 nm, which needs to be converted into meters. Since 1 nm = 1 × 10^-9 m, the wavelength is equal to 325 × 10^-9 m.
Now, we can rearrange the formula to solve for the number of photons:
Number of Photons = Energy × Wavelength / (Planck's constant × Speed of light)
To calculate the number of photons, plug in the given values:
Number of Photons = (0.001 J) × (325 × 10^-9 m) / (Planck's constant × Speed of light)
The value of Planck's constant is 6.63 × 10^-34 J·s, and the value of the speed of light is 3 × 10^8 m/s.
Substituting those values, we get:
Number of Photons = (0.001 J) × (325 × 10^-9 m) / (6.63 × 10^-34 J·s × 3 × 10^8 m/s)
Calculating the numerical value, we find:
Number of Photons ≈ 1.558 × 10^18 photons
Therefore, there are approximately 1.558 × 10^18 photons in a 1.00 mJ burst of radiation with a wavelength of 325 nm.