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

                                      _{38}^{94}Sr- X +v_e+6 

(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] 

    Answer/Explanation

    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]

     
    Answer/Explanation

    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]