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Electric Potential of Hydrogen-like ions

  • Thread starter stevenlu
  • Start date
2
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1. 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,

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

3. The Attempt at a Solution
I try plugging in the data into the equations, but I cannot even start a or b.
 

Answers and Replies

458
0
Show your work, we can't help you if we don't know where you went wrong.
 
2
0
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.
 
458
0
It's asking for the potential energy, not the potential.
 

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