Final answer:
The energy of a photon with a wavelength of 2.45x10-5 nm can be calculated using the formula E = hf, where h is Planck's constant and f is the frequency. By converting the wavelength to frequency using the equation c = λf, we can find the frequency and then calculate the energy. The energy of the photon is 1.342x10-40 kJ/mol.
Step-by-step explanation:
The energy of a photon can be calculated using the formula E = hf, where E is the energy, h is Planck's constant, and f is the frequency of the photon. To convert the wavelength to frequency, we can use the equation c = λf, where c is the speed of light and λ is the wavelength. By substituting the given wavelength of 2.45x10-5 nm (which is equivalent to 2.45x10-11 m) into this equation, we can find the frequency. Once we have the frequency, we can use the formula to calculate the energy of the photon in joules.
Given:
Wavelength (λ) = 2.45x10-11 m
Using the equation c = λf, where c = 3.00x108 m/s
f = c / λ = (3.00x108 m/s) / (2.45x10-11 m) = 1.22x1019 Hz
Next, we can use the formula E = hf to calculate the energy:
E = (6.626x10-34 J·s) x (1.22x1019 Hz) = 8.08x10-15 J
To express the energy numerically in kilojoules per mole, we need to convert the energy in joules to kilojoules and then divide by Avogadro's constant (6.022x1023 mol-1).
Energy per mole = (8.08x10-15 J / 1000) / (6.022x1023 mol-1) = 1.342x10-40 kJ/mol