# IBDP Physics Topic 7.1 – Discrete energy and radioactivity: IB Style Question Bank HL Paper 2

### Question

A sample of waste produced by the reactor contains 1.0 kg of strontium-94 (Sr-94). Sr-94 is radioactive and undergoes beta-minus (β) decay into a daughter nuclide X.

The reaction for this decay is (i) Write down the proton number of nuclide X.      

The graph shows the variation with time of the mass of Sr-94 remaining in the sample. (ii) State the half-life of Sr-94.   

(iii) Calculate the mass of Sr-94 remaining in the sample after 10 minutes.                

Ans

i 39

ii 75 «s»

iii

ALTERNATIVE 1

10 min = 8 1/2 t mass remaining = 1.0 × $$(\frac{1}{2})^8$$ = 3.9 × 10-3 «kg»

ALTERNATIVE 2

decay constant = «$$\frac{In2}{75}$$ = » 9.24 ×10-3 «s-1» mass remaining  10 × e -9.24 ×10-3×600  = 3.9 × 10-3«kg»

Question

The radioactive nuclide beryllium-10 (Be-10) undergoes beta minus (β–) decay to form a stable boron (B) nuclide.

The initial number of nuclei in a pure sample of beryllium-10 is N0. The graph shows how the number of remaining beryllium nuclei in the sample varies with time. An ice sample is moved to a laboratory for analysis. The temperature of the sample is –20 °C.

a.

Identify the missing information for this decay. b.iii.

Beryllium-10 is used to investigate ice samples from Antarctica. A sample of ice initially contains 7.6 × 1011 atoms of beryllium-10. The present activity of the sample is 8.0 × 10−3 Bq.

Determine, in years, the age of the sample.

c.iv.

The temperature in the laboratory is higher than the temperature of the ice sample. Describe one other energy transfer that occurs between the ice sample and the laboratory.

## Markscheme

a.

$$_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}} \to _{{\mkern 1mu} {\mkern 1mu} 5}^{10}{\text{B}} + _{ – 1}^{\,\,\,0}{\text{e}} + {\overline {\text{V}} _{\text{e}}}$$

antineutrino AND charge AND mass number of electron $$_{ – 1}^{\,\,\,0}{\text{e}}$$, $$\overline {\text{V}}$$

conservation of mass number AND charge $$_{\,\,5}^{10}{\text{B}}$$, $$_{{\mkern 1mu} {\mkern 1mu} 4}^{10}{\text{Be}}$$

Do not accept V.

Accept $${\bar V}$$ without subscript e.[2 marks]

b.iii.

λ «= $$\frac{{\ln 2}}{{1.4 \times {{10}^6}}}$$» = 4.95 × 10–7 «y–1»

rearranging of A = λN0eλt to give –λt = ln $$\frac{{8.0 \times {{10}^{-3}} \times 365 \times 24 \times 60 \times 60}}{{4.95 \times {{10}^{-7}} \times 7.6 \times {{10}^{11}}}}$$ «= –0.400»

t = $$\frac{{ – 0.400}}{{ – 4.95 \times {{10}^{ – 7}}}} = 8.1 \times {10^5}$$ «y»

Allow ECF from MP1[3 marks]

c.iv.

from the laboratory to the sample

conduction – contact between ice and lab surface.

OR

convection – movement of air currents

Must clearly see direction of energy transfer for MP1.

Must see more than just words “conduction” or “convection” for MP2.[2 marks]