Multiple Choice
What is the minimum frequency of light required to remove an electron from a titanium metal sample, given that the binding energy of titanium is 3.14 × 10^3 kJ/mol?
9. Quantum Mechanics
The Energy of Light
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How much energy (in joules) is contained in 1.00 mole of 552 nm photons?
A
2.17 x 10^5 J
B
3.61 x 10^5 J
C
1.23 x 10^5 J
D
4.50 x 10^5 J
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 x 10^-34 J·s), c is the speed of light (3.00 x 10^8 m/s), and \( \lambda \) is the wavelength of the photon.
Convert the given wavelength from nanometers to meters. Since 1 nm = 1 x 10^-9 m, 552 nm is equivalent to 552 x 10^-9 m.
Substitute the values of h, c, and \( \lambda \) into the equation to calculate the energy of a single photon: E = \( \frac{(6.626 \times 10^{-34} \text{ J·s})(3.00 \times 10^8 \text{ m/s})}{552 \times 10^{-9} \text{ m}} \).
Calculate the energy of one mole of photons by multiplying the energy of a single photon by Avogadro's number (6.022 x 10^23 mol^-1), since one mole contains that many photons.
Finally, express the result in joules to find the total energy contained in 1.00 mole of 552 nm photons.
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