Electric Potential of Hydrogen-like ions

AI Thread Summary
The discussion centers on calculating the electric potential and kinetic energy of a hydrogen-like ion, specifically the Li+2 ion with Z = 3. The user attempts to apply the Bohr model equations to find the radius of the electron's orbit and the potential energy, but confuses potential with potential energy. The correct approach involves using the formula for potential energy in the context of the electron-nucleus system, which is not clearly followed in the user's calculations. The thread emphasizes the need to clarify the distinction between potential and potential energy to resolve the homework problem effectively. Understanding these concepts is crucial for accurately determining the energies associated with the allowed orbits.
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Homework Statement


Hydrogen-like ions consist of one electron and a nucleus of a charge Ze (Z - the number of protons in the nucleus and e - the charge of an electron). The Bohr model of a hydrogen-like ion states that the single electron can exist only in certain allowed orbits around the nucleus. The radius of each Bohr orbit is: r=(a*n^2)/Z, where a = 0.0529 nm (Bohr'r radius of a hydrogen atom for n=1), n = 1, 2, 3, ... - the number of an allowed orbit (excited level), and Z - the number of protons in the nucleus.

Note: Express your answers in electron volts. Assume that potential energy PE = 0 at r = (infinity). For the hydrogen-like ion with Z = 3, that is Li+2 ion, determine the potential energy of the electron-nucleus system when the electron is in the

(a) first allowed orbit, n = 1;
(b) second allowed orbit, n = 2;
(c) when the electron has escaped from the atom, r = (infinity).

Determine the kinetic energy of the electron in the
(d) first allowed orbit, n = 1;
(e) second allowed orbit,

Homework Equations


r=(a*n^2)/Z
V=kQ/r

The Attempt at a Solution


I try plugging in the data into the equations, but I cannot even start a or b.
 
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Show your work, we can't help you if we don't know where you went wrong.
 
For a, I've tried doing the following:
r=(a*n^2)/Z
r=(0.0529*1^2)/3
r=0.0176333333

V=(kQ)/r
V=(8.99e9*1.6e-19)/0.0176
V=8.17272727e-8

eV=V/1.6e-19
eV=8.1727e-8/1.6e-19
eV=510,793,750,000

However, I do not think my attempt is correct at all.
 
It's asking for the potential energy, not the potential.
 
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