Chapter 6: Q25DQ (page 1353)

Compare the allowed energy levels for the hydrogen atom, the particle in a box, and the harmonic oscillator. What are the values of the quantum number n for the ground level and the second excited level of each system?

Expert verified

Quantum number n for

Hydrogen atom of ground level n = 1 and second excited state n = 3

Particle in box of ground level n = 1 and second excited state n = 3

Harmonic oscillator of ground level n = 0 and second excited state n = 2

Step by step solution

For the hydrogen atom,

The ground level corresponds to n = 1 and the second excited state corresponds to n = 3.

For the particle in a box system

The ground level corresponds to n = 1 and the second excited state corresponds to n = 3.

For the harmonic oscillator system

The ground level corresponds to n = 0 and the second excited state corresponds to n = 2.

Thus, the quantum number n for

Hydrogen atom of ground level n = 1 and second excited state n = 3

Particle in box of ground level n = 1 and second excited state n = 3

Harmonic oscillator of ground level n = 0 and second excited state n = 2

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