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A hydrogen atom in an excited state can be ionized with less energy than when it is in its ground state. What is n for a hydrogen atom if 0.278 eV of energy can ionize it?

Question

A hydrogen atom in an excited state can be ionized with less energy than when it is in its ground state. What is n for a hydrogen atom if 0.278 eV of energy can ionize it?

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Solution

To determine the value of n for a hydrogen atom, we can use the formula for the energy levels of a hydrogen atom:

E = -13.6/n^2 eV

where E is the energy of the atom and n is the principal quantum number.

Given that 0.278 eV of energy is required to ionize the hydrogen atom, we can set up the equation:

0.278 = -13.6/n^2

To solve for n, we can rearrange the equation:

n^2 = -13.6/0.278

n^2 ≈ -48.92

Since the principal quantum number (n) must be a positive integer, we can conclude that n is not a valid value in this case.

This problem has been solved

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