Table of contents

1. Intro to General Chemistry3h 48m
2. Atoms & Elements4h 16m
3. Chemical Reactions4h 10m
4. BONUS: Lab Techniques and Procedures1h 38m
5. BONUS: Mathematical Operations and Functions48m
6. Chemical Quantities & Aqueous Reactions3h 53m
7. Gases3h 49m
8. Thermochemistry2h 37m
9. Quantum Mechanics2h 58m
10. Periodic Properties of the Elements3h 9m
11. Bonding & Molecular Structure3h 29m
12. Molecular Shapes & Valence Bond Theory1h 57m
13. Liquids, Solids & Intermolecular Forces2h 23m
14. Solutions3h 1m
15. Chemical Kinetics2h 53m
16. Chemical Equilibrium2h 29m
17. Acid and Base Equilibrium5h 1m
18. Aqueous Equilibrium4h 47m
19. Chemical Thermodynamics1h 50m
20. Electrochemistry2h 42m
21. Nuclear Chemistry2h 36m
22. Organic Chemistry5h 7m
23. Chemistry of the Nonmetals2h 39m
24. Transition Metals and Coordination Compounds3h 16m

9. Quantum Mechanics

The Energy of Light

General Chemistry

9. Quantum Mechanics

The Energy of Light

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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?

9.56 × 10^13 Hz

7.87 × 10^14 Hz

1.23 × 10^15 Hz

4.75 × 10^14 Hz

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Verified step by step guidance

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.