How many lines of atoms would you expect to see on the collector plate of a Stern-Gerlach apparatus if the experiment is done with (a) lithium and (b) beryllium? Explain.

검증된 단계별 안내

Understand the Stern-Gerlach experiment: The Stern-Gerlach apparatus is used to measure the spin of particles. When a beam of atoms passes through a non-uniform magnetic field, the magnetic moment of the atoms interacts with the field, causing the beam to split into discrete lines based on the spin quantum number (m_s).

Determine the electronic configuration of lithium (Li): Lithium has an atomic number of 3, so its electronic configuration is 1s² 2s¹. The outermost electron in the 2s orbital determines the spin behavior. Since this is a single unpaired electron, the spin quantum number (s) is 1/2, and the possible values of m_s are +1/2 and -1/2. This means the beam will split into 2 lines.

Determine the electronic configuration of beryllium (Be): Beryllium has an atomic number of 4, so its electronic configuration is 1s² 2s². Both electrons in the 2s orbital are paired, meaning their spins cancel each other out. The net spin quantum number (s) is 0, and there are no possible values for m_s. This means the beam will not split, and only 1 line will appear.

Summarize the results: For lithium, the beam splits into 2 lines due to the unpaired electron in the 2s orbital. For beryllium, the beam does not split because all electrons are paired, resulting in no net spin.

Conclude: The number of lines observed on the collector plate depends on the spin quantum number of the outermost electrons. Lithium produces 2 lines, while beryllium produces 1 line.

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주요 개념

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Stern-Gerlach Experiment

The Stern-Gerlach experiment demonstrates the quantization of angular momentum. It involves passing a beam of particles, such as atoms, through a non-uniform magnetic field, which causes the particles to deflect based on their magnetic moments. This deflection reveals the discrete orientations of the particles' spins, illustrating fundamental principles of quantum mechanics.

Atomic Spin

Atomic spin is a quantum property of particles, such as electrons, that describes their intrinsic angular momentum. For atoms, the total spin is determined by the arrangement of electrons and their respective spins. In the context of the Stern-Gerlach experiment, the spin states of the atoms lead to distinct deflections, which can be counted to determine how many lines appear on the collector plate.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom's orbitals. Different elements have unique configurations that influence their magnetic properties and, consequently, their behavior in a magnetic field. For lithium and beryllium, the number of unpaired electrons affects the number of observable spin states in the Stern-Gerlach experiment, leading to different expected outcomes in terms of lines on the collector plate.