Radius of He+ Ion in Bohr Orbit 3.0

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In summary, the radius of a singly ionized helium atom in Bohr orbit number 3.0 can be calculated using the equation r=n^2*a0, with a different value for the nuclear charge (z=2) compared to the hydrogen atom.
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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.
 
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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.
 
  • #3


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.
 

Related to Radius of He+ Ion in Bohr Orbit 3.0

1. What is the radius of He+ ion in Bohr orbit 3.0?

The radius of He+ ion in Bohr orbit 3.0 is approximately 5.29 x 10^-11 meters.

2. How is the radius of He+ ion in Bohr orbit 3.0 calculated?

The radius of He+ ion in Bohr orbit 3.0 is calculated using the Bohr radius formula, which is given by r = n^2 * h^2 / 4π^2 * μ * e^2, where n is the principal quantum number, h is Planck's constant, π is pi, μ is the reduced mass of the system, and e is the elementary charge.

3. What is the significance of the radius of He+ ion in Bohr orbit 3.0?

The radius of He+ ion in Bohr orbit 3.0 is significant because it represents the distance between the nucleus and the electron in the third energy level of a Helium ion. It also helps to determine the size and stability of the atom.

4. How does the radius of He+ ion in Bohr orbit 3.0 compare to other atoms?

The radius of He+ ion in Bohr orbit 3.0 is smaller than the radius of other atoms, such as Hydrogen or Helium in their ground state. This is because the Helium ion has a higher nuclear charge, which results in a stronger attraction between the nucleus and the electron, causing the electron to be pulled closer to the nucleus.

5. Can the radius of He+ ion in Bohr orbit 3.0 change?

Yes, the radius of He+ ion in Bohr orbit 3.0 can change if the energy level of the electron changes. When the electron moves to a higher energy level, the radius increases, and when it moves to a lower energy level, the radius decreases. This change in radius is due to the change in the distance between the nucleus and the electron.

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