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.