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

Previous problemNext problem

Struggling with General Chemistry?

Join thousands of students who trust us to help them ace their exams!Watch the first video

Multiple Choice

Assuming that radiation with λ=15.0 cm is used, and that all the energy is converted to heat, with 4.184 J 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 a 300 g sample of water by 1.00 °C?

1.20 x 10^23 photons

5.00 x 10^21 photons

3.00 x 10^24 photons

2.50 x 10^22 photons

Previous problemNext problem

Verified step by step guidance

First, calculate the total energy required to raise the temperature of the 300 g sample of water by 1.00 °C. Use the formula: \( E = m \cdot c \cdot \Delta T \), where \( m \) is the mass of the water (300 g), \( c \) is the specific heat capacity of water (4.184 J/g°C), and \( \Delta T \) is the change in temperature (1.00 °C).

Next, determine the energy of a single photon using the wavelength \( \lambda = 15.0 \) cm. Use the equation \( E_{photon} = \frac{hc}{\lambda} \), where \( h \) is Planck's constant \( 6.626 \times 10^{-34} \) J·s, \( c \) is the speed of light \( 3.00 \times 10^{8} \) m/s, and \( \lambda \) is the wavelength converted to meters (0.15 m).

Calculate the energy of a single photon using the values from the previous step. Substitute \( h \), \( c \), and \( \lambda \) into the equation \( E_{photon} = \frac{hc}{\lambda} \) to find the energy of one photon.

Determine the number of photons required by dividing the total energy needed to raise the temperature of the water by the energy of a single photon. Use the formula: \( N = \frac{E_{total}}{E_{photon}} \), where \( E_{total} \) is the energy calculated in the first step and \( E_{photon} \) is the energy of a single photon calculated in the third step.

Finally, compare the calculated number of photons \( N \) with the given options to identify the correct answer.