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

De Broglie Wavelength

General Chemistry

9. Quantum Mechanics

De Broglie Wavelength

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Multiple Choice

Consider an atom traveling at 1% of the speed of light. The de Broglie wavelength of the atom is found to be 3.32 × 10⁻³ pm. Which element is this?

Carbon

Hydrogen

Uranium

Helium

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Verified step by step guidance

First, understand the de Broglie wavelength formula: \( \lambda = \frac{h}{mv} \), where \( \lambda \) is the wavelength, \( h \) is Planck's constant \((6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s})\), \( m \) is the mass of the particle, and \( v \) is the velocity of the particle.

Convert the given de Broglie wavelength from picometers to meters: \( 3.32 \times 10^{-3} \text{ pm} = 3.32 \times 10^{-15} \text{ m} \).

Calculate the velocity of the atom, which is 1% of the speed of light. The speed of light \( c \) is approximately \( 3.00 \times 10^8 \text{ m/s} \), so \( v = 0.01 \times c = 3.00 \times 10^6 \text{ m/s} \).

Rearrange the de Broglie equation to solve for mass: \( m = \frac{h}{\lambda v} \). Substitute the known values: \( m = \frac{6.626 \times 10^{-34} \text{ m}^2 \text{ kg/s}}{3.32 \times 10^{-15} \text{ m} \times 3.00 \times 10^6 \text{ m/s}} \).

Compare the calculated mass with the atomic masses of the given elements. The mass should be closest to the atomic mass of Uranium, which is approximately \( 238 \text{ u} \) (where \( 1 \text{ u} = 1.660539 \times 10^{-27} \text{ kg} \)).