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# Singly ionized helium (He $^{+} )$ is a hydrogen-like atom. Determine the energy in eV required to raise a $\mathrm{He}^{+}$ electron from the $n=1$ to the $n=2$ energy level.

## $E = 40.8 \, \rm eV$

Atomic Physics

Nuclear Physics

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### Video Transcript

in this exercise, we have to calculate the energy required to raise a helium atom from the ground state. That's n equals one to the second energy level. S So what I'm gonna do here to calculate the energy level of the first state and of the second state? Okay. And then I'm gonna with these two informations that can calculate the energy required trees from one state to the other. So I noticed that the ionized helium is either gonna like Adam because there's only one electrons orbiting the nucleus. And in this case, the helium has an atomic number equals to two. Okay, so remember that the energy of the Anthony Girolamo of a hydrogen like Adam is given by minus 13.6 z squared over and square at extra votes. So we have that for the helium Z equals two. So minus 13.6 times four over and square, which is minus 54.4 electoral votes. The red by and square. That's the D energy of the IMF energy level of the heat. Him, Adam So have for the first energy level for the ground state that's just minus 54.4 electoral votes. And for the second state, that's minus 54.4, divided by four. Okay, Okay. I'm gonna leave me like that for for a minute and notice that the energy required to raise the Adam from the first a firm form the first state from the ground state to the second state is e equals two, two miners he want. Yeah, that's just from conservation of energy. So this is 54 went four times one minus 1/4. So this is 54.4 times three, divided by four, which is 40.8 electoral votes. Okay, so this is the energy required to raise the V a helium atom.