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Chapter 36: Problem 25

What are the possible \(j\) values for a hydrogen atom in the \(3 D\) state?

Short Answer

Expert verified
The possible \(j\) values for a hydrogen atom in the 3D state are \(1.5\) and \(2.5\)

Step by step solution

01

Identify quantum numbers from atomic state

The atomic state given is \(3D\). From this, we identify the principal quantum number \(n = 3\) and the orbital quantum number \(l = 2\) (since D corresponds to \(l = 2\)).
02

Calculate possible j values

The quantum mechanical rule for the total angular momentum quantum number \(j\) states that \(j\) can range from \(l - 1/2\) to \(l + 1/2\) in steps of 1. So, for \(l = 2\), the possible values of \(j\) are \(2 - 1/2 = 1.5\) and \(2 + 1/2 = 2.5\).

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Most popular questions from this chapter

A hydrogen atom is in an \(l=2\) state. What are the possible angles its orbital angular momentum vector can make with a given axis?

A selection rule for the infinite square well allows only those transitions in which \(n\) changes by an odd number. Suppose an infinite square well of width 0.200 nm contains an electron in the \(n=4\) state. (a) Draw an energy-level diagram showing all allowed transitions that could occur as this electron drops toward the ground state, including transitions from lower levels that could be reached from \(n=4 .\) (b) Find all the possible photon energies emitted in these transitions.

A hydrogen atom is in the \(6 f\) state. Find (a) its energy and (b) the magnitude of its orbital angular momentum.

A selection rule for the infinite square well allows only those transitions in which \(n\) changes by an odd number. Suppose an infinite square well of width \(0.200 \mathrm{nm}\) contains an electron in the \(n=4\) state. (a) Draw an energy-level diagram showing all allowed transitions that could occur as this electron drops toward the ground state, including transitions from lower levels that could be reached from \(n=4 .\) (b) Find all the possible photon energies emitted in these transitions.

The electron in a hydrogen atom is somewhat like a particle confined to a three-dimensional box. In the atom, what plays the role of the confining box?
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