1. Hydrogen is the simplest atom in the universe, thus it is the most commonly used example for delving into the quantum world. The energy levels of hydrogen can be calculated using the principle quantum number, n, in the equation En = −13.6 eV (1/n 2 ), for n = 1, 2, 3, 4 ... ∞. Recall that eV stands for the energy unit called the electron volt, which relates to joules (J) by the following conversion: 1 eV = 1.602 × 10 −19J.

Question

1. Hydrogen is the simplest atom in the universe, thus it is the most commonly used example for delving into the quantum world. The energy levels of hydrogen can be calculated using the principle quantum number, n, in the equation En = −13.6 eV (1/n 2 ), for n = 1, 2, 3, 4 ... ∞. Recall that eV stands for the energy unit called the electron volt, which relates to joules (J) by the following conversion: 1 eV = 1.602 × 10 −19J.

a. What is the value of principle quantum number, n, for the ground state of hydrogen?
b. Calculate the energy (in eV and in joules) for the ground state of hydrogen. c. Calculate the energy, En, for the first four excited states of the hydrogen atom.

Answer 1

a. Ground state for H atom is for n = 1

b. Substitute n = 1 into the equation of En = −13.6 eV (1/n 2) and make the conversion to J. I don't intend to do the calculation for you.
c. Same as b but the excited states are n = 2 or 3 or 4 etc.
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