Final answer:
The energy of the n = 5 level of a hydrogen atom is -0.544 eV.
Step-by-step explanation:
The energy levels of an electron in a hydrogen atom are given by the equation:
E = -13.6 eV/n^2
where E is the energy in electron volts (eV) and n is the principal quantum number.
The question states that the energy of the n = 1 level is -2.18 x 10^-18 J. We can convert this energy to eV using the conversion factor:
1 J = 6.242 x 10^18 eV
Therefore, the energy of the n = 1 level is:
E = (-2.18 x 10^-18 J) x (6.242 x 10^18 eV/J) = -13.59 eV (rounded to two decimal places)
To find the energy of the n = 5 level, we substitute n = 5 into the equation:
E = -13.6 eV/n^2 = -13.6 eV/(5^2) = -13.6 eV/25 = -0.544 eV (rounded to three decimal places)
Therefore, the energy of the n = 5 level is -0.544 eV.