IB Physics HL E.3 Radioactive Decay Question Bank

[Maximum number: 10]

The binding energy of the stable nuclide ${ }_{54}^{131} \mathrm{Xe}$ is 1.105 GeV .

(a)

Outline what is meant by binding energy.

[ 1 ]

(b)

Calculate, in $\mathrm{GeV} \mathrm{c}^{-2}$ , the mass of a nucleus of ${ }_{54}^{131} \mathrm{Xe}$ .

[ 2 ]

Use of Binding energy = mass of separate nucleons - mass of nucleus
$\begin{aligned} \text { « } 1105=54 \times 938+77 \times 940-M c^{2} \text { » } M=122 \text { « } \mathrm{GeVc}^{-2} \text { » } \end{aligned}$

Do not allow BCA.

Award ECF from using binding energy with incorrect sign.

An answer that doesn't include binding energy scores [0].

(c)

$\quad{ }_{54}^{133} \mathrm{Xe}$ and ${ }_{54}^{131} \mathrm{Xe}$ are two isotopes of xenon.

[ 3 ]

(i)

Outline what is meant by isotopes.

[ 2 ]

(ii)

$\quad{ }_{54}^{133} \mathrm{Xe}$ is radioactive. Suggest how the binding energy per nucleon for ${ }_{54}^{131} \mathrm{Xe}$ compares with that of ${ }_{54}^{133} \mathrm{Xe}$ .

[ 1 ]

binding energy per nucleon is a measure of stability so ${ }_{54}^{131} \mathrm{Xe}$ has the greater binding
energy per nucleon

Correct mention of stability required to award the mark.

Marking guidance:

Allow opposite comment for Xe 133.

(d)

The graph shows the variation with time of the activity of a pure sample of ${ }_{54}^{133} \mathrm{Xe}$ .
$A / 10^{7} \mathrm{~Bq}$

[ 4 ]

(i)

Estimate the half-life of ${ }_{54}^{133} \mathrm{Xe}$ .

[ 1 ]

(ii)

Calculate the activity of the sample after 25 days as a fraction of the initial activity.

[ 3 ]

ALTERNATIVE 1

decay constant in range 0.128 to 0.133 «days ${ }^{-1}$ »
$\frac{A}{A_{0}}=e^{-\lambda \times 25}$

answer in range 0.036 to 0.040

ALTERNATIVE 2
$n=\frac{25}{5.3}=\ll 4.7 \text { half lives } \gg$ $\frac{A}{A_{0}}=0.5^{4.7}$

answer in range 0.036 to 0.040

Marking guidance:

Allow ECF from (c)(i)

IB Physics HL E.3 Radioactive Decay Question Bank

Exam points

Covered syllabus points

Covered syllabus points

E.3 Radioactive decay question 1

Question (a)

Question (b)

Question (c)

Question (i)

Question (ii)

Question (d)

Question (i)

Question (ii)