55Q8 The statements in the following list a refer to the hydrogen atom. Each sta

Question

55Q8

The statements in the following list a refer to the hydrogen atom. Each statement is prefaced by a label in square brackets which indicates whether the statement is to be judged according to the Coulomb model or according to more exact theories beyond the Coulomb model. Check the boxes of the THREE TRUE statements in the following list: [Coulomb model] All hydrogen atom energy eigenfunctions with n > 1 have at least one radial node. [Coulomb model] The fact that hydrogen atom energy eigenfunction are proportional to spherical harmonics is a consequence of the Coulomb potential energy function being independent of the angular coordinates theta and phi, and has nothing to do with the precise 1/r form of the Coulomb potential energy function. [Coulomb model] Quantization of energy in a hydrogen atom occurs because the radial function cannot be allowed to diverge as r rightarrow infinity. [Beyond Coulomb model] In the fine structure of the hydrogen atom spectrum, a state with quantum numbers n, l and j = l + 1/2 has a slightly lower energy than a state with quantum numbers n, l and j = t - 1/2 [Beyond Coulomb model] Fine structure corrections lower the energy of the ground state of a hydrogen atom by a factor of order 0.001% rather than by 1%.

Explanation / Answer

statement 3, 4 and 5 are TURE statements.

statement 4: spin down is having higher energy than spin up state. so the statement is correct.

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