Calculate the wavelength of light if 1.50 mol of photons has an energy of 125 kJ.
6.02x10^23 things=1.00 mol(things)
c=3.00x10^8 m/sec
h=6.626x10^-34 J sec
To calculate the wavelength of light, we can use the equation:
E = hc/λ
where:
E is the energy of the photons,
h is Planck's constant,
c is the speed of light, and
λ is the wavelength of light.
Given that 1.50 mol of photons has an energy of 125 kJ, we need to convert the energy from kJ to J:
125 kJ = 125,000 J
We can now rearrange the equation to solve for the wavelength:
λ = hc/E
Substituting the given values:
λ = (6.626x10^-34 J sec * 3.00x10^8 m/sec) / (125,000 J)
Simplifying:
λ = (1.9888x10^-27 J m) / (125,000 J)
Calculating:
λ = 1.590x10^-32 m
Therefore, the wavelength of light is approximately 1.590x10^-32 meters.
To calculate the wavelength of light, we can use the formula:
wavelength = c * h / E
Where:
wavelength is the wavelength of light in meters,
c is the speed of light, which is 3.00 * 10^8 m/s,
h is Planck's constant, which is 6.626 * 10^-34 J·s (Joule-seconds),
E is the energy of the photons in Joules.
First, let's convert the energy from kilojoules to joules. Since 1 kJ = 1000 J, the energy is 125 kJ = 125,000 J.
Next, we can determine the number of photons by using Avogadro's number (6.02 * 10^23 photons = 1 mol). So 1.50 mol of photons is equal to 1.50 * 6.02 * 10^23 photons.
Now, we can calculate the energy per photon by dividing the total energy by the number of photons:
Energy per photon = Total energy / Number of photons
Energy per photon = 125,000 J / (1.50 * 6.02 * 10^23 photons)
Next, we can substitute the values into the wavelength formula:
wavelength = (3.00 * 10^8 m/s) * (6.626 * 10^-34 J·s) / (Energy per photon)
Finally, we can calculate the wavelength by plugging in the value for the energy per photon we calculated:
wavelength = (3.00 * 10^8 m/s) * (6.626 * 10^-34 J·s) / (Energy per photon)
Simply solve this equation and you will get the wavelength of light in meters.
energy per photon=125,000/6.02E-23
Energy per phonton= h*f=hc/wavelength
then
wavelength=hc/energyperphoton