a microwave oven uses electromagnetic radiation with a wavelength of 3.00x10^6 nm. calculate energy (in joules) of 1.65 moles of photons of this radiation.
E = hc/wavelength. Wavelength must be in m and E is in joules for ONE photon. So for 1.65 moles of photons that will be multiplied by (6.022E23 x 1.65).
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To calculate the energy of photons, you can use the equation:
E = h * c / λ
Where:
E is the energy of the photons,
h is the Planck's constant (6.62607015 × 10^-34 J·s),
c is the speed of light (2.998 × 10^8 m/s),
and λ is the wavelength of the photons in meters.
First, you need to convert the wavelength from nanometers (nm) to meters (m):
Wavelength in meters (m) = Wavelength in nanometers (nm) / 1,000,000,000
So, the wavelength in meters would be:
Wavelength in meters = 3.00 × 10^6 nm / 1,000,000,000
Now, you can calculate the energy of photons using the given values:
E = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (3.00 × 10^6 nm / 1,000,000,000)
Next, you need to convert the number of moles to the number of photons. Since 1 mole of a substance contains Avogadro's number (6.022 × 10^23) of particles (atoms, molecules, or photons), you can multiply the number of moles by Avogadro's number to get the number of photons:
Number of photons = Number of moles * Avogadro's number
Number of photons = 1.65 moles * 6.022 × 10^23
Finally, you can substitute the calculated values into the equation to find the energy:
E = (6.62607015 × 10^-34 J·s * 2.998 × 10^8 m/s) / (3.00 × 10^6 nm / 1,000,000,000) * (1.65 moles * 6.022 × 10^23)
Solve this equation to find the energy of 1.65 moles of photons.