Multiple Choice
What is the total energy (in kJ) of 1.0 mol of photons with a frequency of 2.75 × 10^14 Hz?
9. Quantum Mechanics
The Energy of Light
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How much energy is contained in one mole of X-ray photons with a wavelength of 0.280 nm in kJ/mol?
A
1.23 x 10^3 kJ/mol
B
4.43 x 10^5 kJ/mol
C
2.98 x 10^4 kJ/mol
D
5.67 x 10^2 kJ/mol
Verified step by step guidance1
First, understand that the energy of a photon can be calculated using the equation: \( E = \frac{hc}{\lambda} \), where \( E \) is the energy of the photon, \( h \) is Planck's constant \( (6.626 \times 10^{-34} \text{ J s}) \), \( c \) is the speed of light \( (3.00 \times 10^8 \text{ m/s}) \), and \( \lambda \) is the wavelength of the photon.
Convert the given wavelength from nanometers to meters. Since 1 nm = \( 1 \times 10^{-9} \) m, the wavelength \( \lambda = 0.280 \text{ nm} \) is equivalent to \( 0.280 \times 10^{-9} \text{ m} \).
Substitute the values of \( h \), \( c \), and \( \lambda \) into the energy equation: \( E = \frac{(6.626 \times 10^{-34} \text{ J s})(3.00 \times 10^8 \text{ m/s})}{0.280 \times 10^{-9} \text{ m}} \). This will give you the energy of one photon in joules.
To find the energy contained in one mole of photons, multiply the energy of a single photon by Avogadro's number \( (6.022 \times 10^{23} \text{ mol}^{-1}) \). This will convert the energy from joules per photon to joules per mole.
Finally, convert the energy from joules per mole to kilojoules per mole by dividing by 1000, since 1 kJ = 1000 J. This will give you the energy in kJ/mol.
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