Ground State of Helium

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The diagram on the left shows the energy levels that electrons in helium are allowed to occupy as horizontal lines. Energy levels with the quantum number l = 0, shown in black, can contain two electrons. Energy levels with l = 1, shown in blue, can contain six electrons. To get the ground state of the helium atom, we put one spin-up and one spin-down electron into the lowest available energy level. The image on the right is the electron probability density in a helium atom in its ground state. In the quantum mechanical atom, we cannot know what the two electrons are doing at any instant in time. We only know the probability of finding one of them at a given point in space. The probability density cloud is centered on the nucleus, and the darker shade of blue indicates regions of higher probability. The presence of the two electrons will cause the charge probability density cloud shown in the right half of the figure to expand; but this is then offset by the fact that the nucleus now contains two, rather than one, positively charged protons. This larger nuclear charge ends up causing the size of helium to actually be smaller than that of the hydrogen atom. (Unit: 6)