A particle in the first excited state of a one-dimensional infinite potential energy well (with U = 0 inside the well) has an energy of 6.0 eV. What is the energy of this particle in the ground state?

The energy of this particle in the ground state is E₁=1.5 eV.

Explanation:

The energy of a particle of mass m in the nth energy state of an infinite square well potential with width L is:

In the ground state (n=1). In the first excited state (n=2) we are told the energy is E₂= 6.0 eV. If we replace in the above equation we get that:

So we can rewrite the energy in the ground state as:

Finally

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