UGPhysics

575

Modern Physics

Atomic Physics

Atomic and Molecular Physics

A certain atom's ${}^{3} \mathrm{P}_{2}$ energy level is found to split into five sublevels, with the ratio of the intervals between adjacent sublevels being $9: 7: 5: 3$. Using the interval rule, determine the nuclear spin quantum number $I$ of this atom and the total atomic angular momentum quantum number $F$ corresponding to each sublevel. Find the nuclear spin quantum number $I$.

The rule for hyperfine level intervals is: for a given $J$ value, the interval between two adjacent hyperfine sublevels is proportional to the larger of the quantum numbers $F$ of the two sublevels. Since the total atomic angular momentum quantum numbers are $F = I + J, I + J - 1, \ldots, |I - J|$, When $I \geqslant J$, there are $2J+1$ sublevels; when $I < J$, there are $2I+1$ sublevels. There are 5 sublevels, and since $J = 2$, we have $2J+1 = 5$. This implies $I \geqslant 2$, so the quantum numbers $F = I+2, I+1, I, I-1, I-2$. According to the interval rule, $(I+2):(I+1): I:(I-1)= …

\boxed{\frac{5}{2}}

NV

false

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Laws Application

576

Modern Physics

Atomic Physics

Atomic and Molecular Physics

If the energy of a photon is equal to the rest energy of an electron, what is the frequency of this photon?

The rest energy of an electron is \(m_{\mathrm{e}} c^{2} = 8.187 \times 10^{-14} \mathrm{~J} = 0.5110 \mathrm{~MeV}\). \\ Therefore, the frequency of a photon with energy equal to the rest energy of an electron is \[ \nu = \frac{m_{\mathrm{e}} c^{2}}{h} = 1.2356 \times 10^{20} \mathrm{~Hz}. \]

\boxed{1.2356 \times 10^{20}}

NV

\text{Hz}

false

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