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

Assuming that radiation with λ = 15.0 cm is used, that all the energy is converted to heat, and that 4.184 J is needed to raise the temperature of 1.00 g of water by 1.00 °C, how many photons are necessary to raise the temperature of 250 g of water by 1.00 °C?

2.50 x 10^22 photons

5.00 x 10^22 photons

1.25 x 10^22 photons

7.50 x 10^22 photons

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Verified step by step guidance

Calculate the total energy required to raise the temperature of 250 g of water by 1.00 °C using the specific heat capacity of water. The formula is: \( q = m \cdot c \cdot \Delta T \), where \( q \) is the heat energy, \( m \) is the mass of water, \( c \) is the specific heat capacity (4.184 J/g°C), and \( \Delta T \) is the temperature change.

Substitute the given values into the formula: \( q = 250 \text{ g} \cdot 4.184 \text{ J/g°C} \cdot 1.00 \text{ °C} \). Calculate \( q \) to find the total energy required.

Determine the energy of a single photon using the equation \( E = \frac{hc}{\lambda} \), where \( h \) 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 in meters. Convert the wavelength from cm to meters before substituting.

Calculate the energy of a single photon by substituting the values into the equation: \( E = \frac{6.626 \times 10^{-34} \text{ J·s} \cdot 3.00 \times 10^8 \text{ m/s}}{0.15 \text{ m}} \).

Determine the number of photons required by dividing the total energy calculated in step 2 by the energy of a single photon calculated in step 4. Use the formula: \( \text{Number of photons} = \frac{q}{E} \).