IB Physics HL E.1 Structure of the Atom Question Bank

[Maximum number: 6]

(a)

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

[ 2 ]

(b)

Bohr modified the Rutherford model by introducing the condition $m v r=n \frac{h}{2 \pi}$ .

Outline the reason for this modification.

[ 3 ]

the electrons accelerate and so radiate energy;
they would therefore spiral into the nucleus/atoms would be unstable

electrons have discrete/only certain energy levels

the only orbits where electrons do not radiate are those that satisfy the Bohr condition $mvr=n\frac{h}{2\pi}$

(c)

Calculate the electron's orbital radius in (c)(ii).

[ 1 ]

$\begin{aligned} r=\frac{(6.63\times10^{-34})^2}{4\pi^2\times8.99\times10^9\times9.11\times10^{-31}\times(1.6\times10^{-19})^2} \\ r=5.3\times10^{-11}\ \mathrm{m} \end{aligned}$

[Maximum number: 2]

This question is in two parts. Part 1 is about kinematics and gravitation. Part 2 is about radioactivity.

Part 1 Kinematics and gravitation

A ball is released near the surface of the Moon at time t=0. The point of release is on a straight line between the centre of Earth and the centre of the Moon. The graph below shows the variation with time t of the displacement s of the ball from the point of release.

(a)

Part 2 Radioactivity

Radium-224 $\left({ }_{88}^{224} \mathrm{Ra}\right)$ is a radioactive nuclide that decays to form radon-220. Radon-220 is itself radioactive and undergoes a further decay. The table shows the series of radioactive nuclides that are formed as the decays proceed. The series ends with a stable isotope of lead.

For the final thallium nuclide, identify the

[ 2 ]

(i)

nucleon number.

[ 1 ]

(ii)

proton number.

[ 1 ]

[Maximum number: 5]

(a)

The diagram represents the three principal spectral lines in the visible region of the spectrum of atomic hydrogen.

The electron in the hydrogen atom can only occupy certain allowed energy levels.

[ 5 ]

(i)

Outline how the spectral lines provide evidence for the existence of these energy levels.

[ 3 ]

(ii)

Determine the difference in energy between the two levels from which electron transitions give rise to the $\mathrm{H}_{\alpha}$ and $\mathrm{H}_{\gamma}$ spectral lines respectively.

[ 2 ]

difference in energy $=hc\left[\frac{1}{\lambda_{\gamma}}-\frac{1}{\lambda_{\alpha}}\right]$ ;
$=6.6 \times 10^{-34} \times 3 \times 10^{8} \times 10^{7} \times 0.0780=1.54 \times 10^{-19} \mathrm{~J}$ ;
or
$E_{\alpha}=\frac{hc}{\lambda_{\alpha}}=3.02 \times 10^{-19} \mathrm{~J}$ or $1.89 \mathrm{~eV}$ ;
$E_{\gamma}=\frac{hc}{\lambda_{\gamma}}=4.56 \times 10^{-19} \mathrm{~J}$ or $2.85 \mathrm{~eV}$ ;
difference in energy $=1.54 \times 10^{-19} \mathrm{~J}$ or $0.963 \mathrm{~eV}$ ;

[Maximum number: 2]

Rutherford constructed a model of the atom based on the results of the alpha particle scattering experiment. Describe this model.

[Maximum number: 3]

The diagram represents the three principal spectral lines in the visible region of the spectrum of atomic hydrogen.

The electron in the hydrogen atom can only occupy certain allowed energy levels.

Outline how the spectral lines provide evidence for the existence of these energy levels.

[Maximum number: 3]

This question is in two parts.

The energies of the principal energy levels in atomic hydrogen measured in eV are given by the expression

E_{n}=-\frac{13.6}{n^{2}} \text { where } n=1,2,3

The visible lines in the spectrum correspond to electron transitions that end at n=2.

Show that the spectral line of wavelength $\lambda=485 \mathrm{~nm}$ is the result of an electron transition from n=4.

energy difference between levels $=\frac{h c}{\lambda e}=\frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{4.85 \times 10^{-7} \times 1.6 \times 10^{-19}}$ ;
=2.55 eV;
$[3.40-2.55]=0.85=\frac{13.6}{n^{2}}$ to give $n^{2}=16$ ;
n=4;

Marking guidance:

Award [3] for reversed argument.

[Maximum number: 2]

The diagram represents the three principal spectral lines in the visible region of the spectrum of atomic hydrogen.

The electron in the hydrogen atom can only occupy certain allowed energy levels.

Determine the difference in energy between the two levels from which electron transitions give rise to the $\mathrm{H}_{\alpha}$ and $\mathrm{H}_{\gamma}$ spectral lines respectively.

difference in energy $=hc\left[\frac{1}{\lambda_{\gamma}}-\frac{1}{\lambda_{\alpha}}\right]$ ;
$=6.6 \times 10^{-34} \times 3 \times 10^{8} \times 10^{7} \times 0.0780=1.54 \times 10^{-19} \mathrm{~J}$ ;
or
$E_{\alpha}=\frac{hc}{\lambda_{\alpha}}=3.02 \times 10^{-19} \mathrm{~J}$ or $1.89 \mathrm{~eV}$ ;
$E_{\gamma}=\frac{hc}{\lambda_{\gamma}}=4.56 \times 10^{-19} \mathrm{~J}$ or $2.85 \mathrm{~eV}$ ;
difference in energy $=1.54 \times 10^{-19} \mathrm{~J}$ or $0.963 \mathrm{~eV}$ ;

[Maximum number: 2]

The diagram shows a simplified energy-balance model for the Earth surface-atmosphere system.

The following data are given:

\begin{aligned} \text { Average albedo of Earth } & =0.30 \\ \text { Average global temperature of the surface } & =288 \mathrm{~K} \\ \text { Average Earth-Sun distance } & =1.5 \times 10^{11} \mathrm{~m} \end{aligned}

The primary energy source of the Sun is the proton-proton (p-p) chain of fusion reactions. Four protons and two electrons produce a helium nucleus together with neutrinos and gamma photons. The overall reaction is:

4{ }_{1}^{1} \mathrm{p}+2{ }_{-1}^{0} \mathrm{e} \rightarrow{ }_{2}^{4} \mathrm{He}+2{ }_{0}^{0} v_{e}+4 \gamma

Outline how the presence of helium in the Sun can be confirmed empirically.

[Maximum number: 3]

(a)

State how the density of a nucleus varies with the number of nucleons in the nucleus.

[ 1 ]

(b)

Show that the nuclear radius of phosphorus-31 $\left({ }_{15}^{31} \mathrm{P}\right)$ is about 4 fm .

[ 1 ]

$R=1.20\times10^{-15}\times31^{\frac{1}{3}}=3.8\times10^{-15}\ \mathrm{m}$

(c)

$\quad{ }_{15}^{32} \mathrm{P}$ is formed when a nucleus of deuterium $\left({ }_{1}^{2} \mathrm{H}\right)$ collides with a nucleus of ${ }_{15}^{31} \mathrm{P}$ . The radius of a deuterium nucleus is 1.5 fm .

[ 1 ]

(i)

State the maximum distance between the centres of the nuclei for which the production of ${ }_{15}^{32} \mathrm{P}$ is likely to occur.

[ 1 ]

[Maximum number: 2]

In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead-207. The distance of closest approach is about:

4\times10^{-14}\ \mathrm{m}

The radius of a nucleus of ${ }_{82}^{207} \mathrm{~Pb}$ is $7.1 \times 10^{-15} \mathrm{~m}$ . Suggest why there will be no deviations from Rutherford scattering in the experiment described above.

[Maximum number: 2]

In an experiment, alpha particles of initial kinetic energy 5.9 MeV are directed at stationary nuclei of lead $\left({ }_{82}^{207} \mathrm{~Pb}\right)$ . Show that the distance of closest approach is about $4 \times 10^{-14} \mathrm{~m}$ .

2e AND 82e seen

OR

$3.2 \times 10^{-19}$ «C» AND $1.312 \times 10^{-17}$ «C» seen
$d=\frac{8.99 \times 10^{9} \times(2 e)(82 e)}{5.9 \times 10^{6} \times e}=3.998 \times 10^{-14} \approx 4 \times 10^{-14}<\mathrm{m} \gg$

Must see either clear substitutions or answer to at least 4 s.f. for MP2.

[Maximum number: 1]

This question is in two parts.

The energies of the principal energy levels in atomic hydrogen measured in eV are given by the expression

E_{n}=-\frac{13.6}{n^{2}} \text { where } n=1,2,3

The visible lines in the spectrum correspond to electron transitions that end at n=2.

Calculate the energy of the level corresponding to n=2.

IB Physics HL E 1 Structure of the Atom Questions

Exam points

Covered syllabus points

Covered syllabus points

Question 1

Question (a)

Question (b)

Question (c)

Question 2

Question (a)

Question (i)

Question (ii)

Question 3

Question (a)

Question (i)

Question (ii)

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question (a)

Question (b)

Question (c)

Question (i)

Question 10

Question 11

Question 12