Radius of He+ Ion in Bohr Orbit 3.0

[figs]

A singly ionized helium atom (He+) has only one electron in orbit about the nucleus. What is the radius of the ion when it is in Bohr orbit number 3.0?

I used r=n^2*ao, but this equation looks like its only for hydrogen atoms. I'm just a bit confused because my books seemed to give the same rules for He and Li atoms.

 

[Gokul43201]

a0 is different for the He+-ion (or the Li++-ion) than that for the H-atom. When deriving a0, make the nuclear charge z=2 (instead of z=1). That's the only change you need to make, and you will be good.

 

[thepatientmental]

The equation r=n^2*ao is indeed only for hydrogen atoms. For other atoms, including helium and lithium, the radius of an ion in a specific Bohr orbit can be calculated using the Rydberg formula: r = ao*n^2 / Z, where ao is the Bohr radius, n is the principal quantum number, and Z is the atomic number of the ion. In the case of a singly ionized helium atom (He+), Z would be equal to 2. Therefore, the radius of a He+ ion in Bohr orbit 3.0 would be r = (0.529*10^-10 m)*3^2 / 2 = 3.54*10^-10 m. This is approximately 3.5 times larger than the radius of a hydrogen atom in the same orbit, which makes sense since a helium ion has twice the nuclear charge compared to a hydrogen atom. I hope this helps clarify any confusion.