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A particle with mass m moves in a 3D potential well described by the Hamiltonian: H = p²/2m + ½ k(x² + y² + z²) + λxyz. With increasing λ, what happens to the energy levels of the particle?
A particle with mass m moves in a 3D potential well described by the Hamiltonian: H = p²/2m + ½ k(x² + y² + z²) + λxyz. With increasing λ, what happens to the energy levels of the particle?
- They all increase equally.
- They decrease equally.
- They split due to perturbation theory. (correct)
- Requires numerical calculations for specific values.
In a nuclear fusion reaction, two deuterium nuclei (²H) collide to form a helium-3 nucleus (³He) and a neutron. Which conservation law limits the possible outcomes of this reaction?
In a nuclear fusion reaction, two deuterium nuclei (²H) collide to form a helium-3 nucleus (³He) and a neutron. Which conservation law limits the possible outcomes of this reaction?
- Momentum
- Energy (correct)
- Charge
- All of the above
An unknown compound exhibits an absorption peak in its UV-Vis spectrum at 280 nm and a strong peak in its ¹H NMR spectrum at 9.7 ppm. Which functional group is most likely present?
An unknown compound exhibits an absorption peak in its UV-Vis spectrum at 280 nm and a strong peak in its ¹H NMR spectrum at 9.7 ppm. Which functional group is most likely present?
- Alcohol
- Aldehyde
- Aromatic ring (correct)
- Amine
CRISPR-Cas9 technology can be used to modify the genome of an organism with high precision. What is the primary role of the Cas9 protein in this process?
CRISPR-Cas9 technology can be used to modify the genome of an organism with high precision. What is the primary role of the Cas9 protein in this process?
El Niño events are associated with warmer than average sea surface temperatures in the equatorial Pacific Ocean. What is the primary mechanism that triggers these events?
El Niño events are associated with warmer than average sea surface temperatures in the equatorial Pacific Ocean. What is the primary mechanism that triggers these events?
A newly discovered organism undergoes mitosis and cytokinesis, resulting in eight genetically identical daughter cells. Which type of cell division is this?
A newly discovered organism undergoes mitosis and cytokinesis, resulting in eight genetically identical daughter cells. Which type of cell division is this?
The rate constant (k) for a first-order reaction doubles when the temperature increases from 25°C to 35°C. Assuming the Arrhenius equation holds, what is the activation energy (Ea) for this reaction?
The rate constant (k) for a first-order reaction doubles when the temperature increases from 25°C to 35°C. Assuming the Arrhenius equation holds, what is the activation energy (Ea) for this reaction?
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