A triply ionized beryllium ion, Be3+ (a beryllium atom with three electrons removed), behaves very much like a hydrogen atom except that the nuclear charge is four times as great. (a) What is the ground-level energy of Be3+? How does this compare to the ground-level energy of the hydrogen atom?

Video transcript

Welcome back, everyone. We are asked to consider a hydrogen like atom with a nuclear charge of Z equals three. We need to calculate two things here. We need to calculate first the energy of the electron in the first excited state. So with a principle number of two of this hydrogen like atom with the nuclear charge of three, and then we need to calculate the ratio between that energy of the electron with the nuclear charge of Z equals three divided by an electron in the first excited state. But this time with the nuclear charge of C equals one, let's start with part one here just finding the energy of our electron in the first excited state. Well, what we can do is we can say that for any energy in any state, our formula is negative 13.6 electron volts times the nuclear charge squared divided by the principle number squared. So for our energy in the first excited state with a principle number of two and a nuclear charge of three, we have negative 13.6 electron volts times three squared divided by two squared which gives us negative 30. electron volts. Now moving on to part two here, let's first calculate this bottom energy. So we need to calculate the energy in the first excited state with a nuclear charge of one. This is going to be negative 13.6 electron volts times one squared divided by two squared. What this gives us is negative 3.4 electron volts. Now we are ready to find the ratio between the first energy that we calculated. And the second energy that we calculated what this gives us is negative 30 0.6 divided by negative 3.4, which gives us a ratio of nine. So we have found the energy of the electron in the first excited states with a nuclear charge of three and the ratio when comparing that to the energy of an electron in the first excited state with a nuclear charge of one, which corresponds to our final answer. Choice of C Thank you all so much for watching. I hope this video helped. We will see you all in the next one.