What is the energy of one mole of photons with a wavelength of 375 nm? (h = 6.63 x 10-34 J • s, N = 6.02 x 1023)
A. 5.30 x 10-19 J
B. 2.39 x 105 J
C. 2.66 x 10-18 J
D. 5.30 x 105 J
E. 1.60 x 106 J
Same formula as before with a slight twist.
E = hc/wavelength gives the energy per photon. Multiply by Avogadro's number, 6.02 x 10^23 to get energy per mole of photons.
To calculate the energy of one mole of photons with a given wavelength, we can use the equation:
E = hc/λ
where E is the energy of the photons, h is Planck's constant (6.63 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 photons.
First, let's convert the wavelength from nanometers (nm) to meters (m). We can do this by dividing the given wavelength by 10^9:
375 nm = 375 x 10^-9 m
Next, let's substitute the values into the equation:
E = (6.63 x 10^-34 J · s) * (3.00 x 10^8 m/s) / (375 x 10^-9 m)
Simplifying the equation:
E = (6.63 x 3.00) * 10^-34+8 / (375 x 10^-9)
E = 19.89 x 10^-26 / 375 x 10^-9
E = 19.89/375 * 10^-26+9
E = 0.05296 * 10^-17
Finally, let's convert the result to scientific notation:
E = 5.296 x 10^-19 J
Therefore, the energy of one mole of photons with a wavelength of 375 nm is approximately 5.30 x 10^-19 J.
Answer choice A, 5.30 x 10^-19 J, is the correct answer.