DP Physics (last assessment 2024)

Question 18M.2.HL.TZ2.9c.ii

Date	May 2018	Marks available	[Maximum mark: 2]	Reference code	18M.2.HL.TZ2.9c.ii
Level	HL	Paper	2	Time zone	TZ2
Command term	Deduce	Question number	c.ii	Adapted from	N/A

c.ii.

[Maximum mark: 2]

18M.2.HL.TZ2.9c.ii

(c.ii)

Using the answer in (b) and (c)(i), deduce that the radius r of the electron’s orbit in the ground state of hydrogen is given by the following expression.

$r = \frac{{{h^2}}}{{4{\pi ^2}k{m_{\text{e}}}{e^2}}}$

[2]

Markscheme

combining v = $\sqrt {\frac{{k{e^2}}}{{{m_{\text{e}}}r}}}$ with m_evr = $\frac{h}{{2\pi }}$ using correct substitution

«eg ${m_e}^2\frac{{k{e^2}}}{{{m_{\text{e}}}r}}{r^2} = \frac{{{h^2}}}{{4{\pi ^2}}}$ »

correct algebraic manipulation to gain the answer

Answer given – look for correct working

Do not allow a bald statement of the answer for MP2. Some further working eg cancellation of m or r must be shown

[2 marks]

Syllabus sections

Additional higher level (AHL)

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics » 12.1 – The interaction of matter with radiation

Additional higher level (AHL) » Topic 12: Quantum and nuclear physics

Question 18M.2.HL.TZ2.9c.ii

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