IB Physics HL D 2 12 Hl Two Charge Potential Energy Questions

Derive two-charge electric potential energy and total orbital energy, then interpret how energy loss changes an electron’s orbit and wavelength.

Exam points

Derive and use the two-charge electric potential energy relation Ep=kq1q2/r, including sign.
Relate changes in two-charge potential energy to total energy and orbital radius.

[Maximum number: 4]

(a)

In a classical model of the singly-ionized helium atom, a single electron orbits the nucleus in a circular orbit of radius r.

[ 4 ]

(i)

Hence, deduce that the total energy of the electron is given by $E_{\mathrm{TOT}}=-\frac{k e^{2}}{r}$ .

[ 2 ]

uses (a)(i) to state $E_{\mathrm{k}}=\frac{k e^{2}}{r} \mathcal{OR}$ states $E_{\mathrm{p}}=-\frac{2 k e^{2}}{r}$ adds $« E_{\mathrm{TOT}}=E_{\mathrm{k}}+E_{\mathrm{p}}=\frac{k e^{2}}{r}-\frac{2 k e^{2}}{r}$ » to get the result

(ii)

In this model the electron loses energy by emitting electromagnetic waves.

Describe the predicted effect of this emission on the orbital radius of the electron.

[ 2 ]

the total energy decreases OR by reference to $E_{\text {TOT }}=-\frac{k e^{2}}{r}$ the radius must also decrease

Award [0] for an answer concluding that radius increases

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IB Physics HL D 2 12 Hl Two Charge Potential Energy Questions question 1

Question (a)

Question (i)

Question (ii)