DP Physics (last assessment 2024)

Question 19N.2.HL.TZ0.b(i)

Date	November 2019	Marks available	[Maximum mark: 2]	Reference code	19N.2.HL.TZ0.b(i)
Level	HL	Paper	2	Time zone	TZ0
Command term	Show that	Question number	b(i)	Adapted from	N/A

b(i).

[Maximum mark: 2]

19N.2.HL.TZ0.b(i)

The Bohr model for hydrogen can be applied to the singly-ionized helium atom. In this model the radius $r$ , in m, of the orbit of the electron is given by $r = 2.7 \times 10^{- 11} \times n^{2}$ where $n$ is a positive integer.

Show that the de Broglie wavelength $λ$ of the electron in the $n = 3$ state is $λ = 5.1 \times 10^{- 10}$ m.

The formula for the de Broglie wavelength of a particle is $λ = \frac{h}{m v}$ .

[2]

Markscheme

with $n = 3, v = « \sqrt{\frac{2 \times 8.99 \times 10^{9} \times {(1.6 \times 10^{- 19})}^{2}}{9.11 \times 10^{- 31} \times 9 \times 2.7 \times 10^{- 11}}} = » 1.44 \times 10^{6} « m s^{- 1} »$ ✔

$λ = \frac{6.63 \times 10^{- 34}}{9.11 \times 10^{- 31} \times 1.44 \times 10^{6}}$ OR $λ = 5.05 \times 10^{- 10} « m »$ ✔

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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 19N.2.HL.TZ0.b(i)

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