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Study E.1 Structure of the atom conceptsOpen the corresponding Concept lesson for explanations, examples and exam connections.

[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 ]

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

[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 $0.963 \mathrm{~eV}$ ;

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IB Physics HL E 1 Structure of the Atom Topic Practice

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