Multiple Choice
Calculate the energy of the green light emitted, per photon, by a mercury lamp with a frequency of 5.49 × 10^14 Hz. Use Planck's constant (h = 6.626 × 10^-34 J·s).
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9. Quantum Mechanics
The Energy of Light
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?
A
9.56 × 10^13 Hz
B
7.87 × 10^14 Hz
C
1.23 × 10^15 Hz
D
4.75 × 10^14 Hz
Verified step by step guidance1
First, understand that the problem involves the photoelectric effect, where light is used to remove an electron from a metal surface. The minimum frequency of light required is related to the binding energy of the metal.
Convert the binding energy from kJ/mol to J/atom. Use the conversion factor: 1 kJ = 1000 J and Avogadro's number (6.022 × 10^23 mol^-1) to find the energy per atom.
Calculate the energy per atom using the formula: \( E = \frac{3.14 \times 10^3 \text{kJ/mol} \times 1000 \text{J/kJ}}{6.022 \times 10^{23} \text{mol}^{-1}} \).
Use the relationship between energy and frequency given by Planck's equation: \( E = h \nu \), where \( E \) is the energy per photon, \( h \) is Planck's constant (6.626 × 10^-34 J·s), and \( \nu \) is the frequency.
Rearrange Planck's equation to solve for frequency: \( \nu = \frac{E}{h} \). Substitute the calculated energy per atom and Planck's constant into this equation to find the minimum frequency of light required.
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