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.      [1]

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.   [1]

(iii) Calculate the mass of Sr-94 remaining in the sample after 10 minutes.                [2]

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.

[2]

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.[3]

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.[2]

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]