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DP IB Physics: HL

Topic Questions

Home / IB / Physics: HL / DP / Topic Questions / 7. Atomic, Nuclear & Particle Physics / 7.1 Discrete Energy & Radioactivity / Structured Questions


7.1 Discrete Energy & Radioactivity

Question 1a

Marks: 3

Transitions between three energy levels in a particular atom give rise to three spectral lines. In decreasing magnitudes, these are f subscript 1, f subscript 2and f subscript 3.

The equation which relates f subscript 1, f subscript 2 and f subscript 3 is:

f subscript 1 equals f subscript 2 plus f subscript 3

(a)
Explain, including through the use of a sketch, how this equation relates f subscript 1f subscript 2 and f subscript 3.

[3]

 

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    Question 1b

    Marks: 5

    A different atom has a complete line emission spectra with a ground state energy of  –10.0 eV. is:

    7-1-ib-sl-hard-sqs-q1b-question

    (b)
    Sketch and label a diagram of the possible energy levels for the atomic line spectra shown.
    [5 marks]
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      Question 1c

      Marks: 3
      (c)
      Explain the significance of an electron at an energy level of 0 eV.
      [3]
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        Key Concepts
        Discrete Energy Levels

        Question 1d

        Marks: 3
        (d)
         
        (i)
        Explain the statement 'the first excitation energy of the hydrogen atom is 10.2 eV'
          [1]
        (ii)
        The ground state of hydrogen is –13.6 eV. Calculate the speed of the slowest electron that could cause this excitation of a hydrogen atom. 
        [2]
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          Question 2a

          Marks: 2

          A radioactive nucleus X presubscript 85 presuperscript 229 undergoes a beta−minus decay followed by an alpha decay to form a daughter nucleus Y presubscript Z presuperscript A.

          (a)
          Write a decay equation for this interaction and hence determine the values of A and Z.
          [2]
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            Question 2b

            Marks: 3

            Thorium, Th presubscript 232 presuperscript 90 decays to an isotope of Radium (Ra) through a series of transformations. The particles emitted in successive transformations are:

             alpha space space beta space space beta space space gamma space space alpha

            (b)
            Determine the resulting nuclide after these successive transformations. 
            [3]
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              Question 2c

              Marks: 3

              Through a combination of successive alpha and beta decays, the isotope of any original nucleus can be formed. 

              (c)
              Explain the simplest sequence of alpha and beta decays required to do this
              [3]
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                Key Concepts
                Decay Equations

                Question 2d

                Marks: 2

                A nucleus of Bohrium Bh presubscript Y presuperscript X decays to Mendelevium Md presubscript 101 presuperscript 255 by a sequence of three alpha particle emissions.

                (d)
                Determine the number of neutrons in a nucleus of Bh presubscript straight Y presuperscript straight X
                [2]
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                  Key Concepts
                  Decay Equations

                  Question 3a

                  Marks: 3

                  The table shows some of the isotopes of phosphorus and, where they are unstable, the type of decay.

                  Isotope P presubscript 15 presuperscript 29 straight P presubscript 15 presuperscript 30 straight P presubscript 15 presuperscript 31 straight P presubscript 15 presuperscript 32 straight P presubscript 15 presuperscript 33
                  Type of decay beta to the power of plus beta to the power of plus stable   beta to the power of minus

                  (a)

                  State whether the isotope straight P presubscript 15 presuperscript 32 is stable or not. If not, determine, with a reason, the type of decay it experiences.

                  [3]

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                    Question 3b

                    Marks: 3

                    The isotope of phosphorus straight P presubscript 15 presuperscript 30 decays into an isotope of silicon, Si presubscript straight Z presuperscript straight A.

                    (b)
                    Write a decay equation for this decay, finding the values of A and Z, and explain why each emission product occurs.
                    [3]

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                      Key Concepts
                      Decay Equations

                      Question 4a

                      Marks: 2

                      The radioactive isotope uranium−238 decays in a decay series to the stable lead−206. 

                      The half−life of U presubscript 92 presuperscript 238 is 4.5 × 109 years, which is much larger than all the other half−lives of the decays in the series.

                      A rock sample, when formed originally, contained 6.0 × 1022 atoms of U presubscript 92 presuperscript 238 and no Pb presubscript 82 presuperscript 206 atoms. At any given time, most of the atoms are either U presubscript 92 presuperscript 238 or Pb presubscript 82 presuperscript 206 with a negligible number of atoms in other forms in the decay series.

                      (a)
                      Sketch on the axes below the variation of number of U presubscript 92 presuperscript 238 atoms and the number of Pb presubscript 82 presuperscript 206 atoms in the rock sample as they vary over a period of 1.0 × 1010 years from its formation. Label your graphs U and Pb.
                      7-1-ib-sl-hard-sqs-q4a-question
                      [2]

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                        Key Concepts
                        Half-Life
                        Decay Curves

                        Question 4b

                        Marks: 2

                        A certain time, t, after its formation, the sample contained twice as many U presubscript 92 presuperscript 238 atoms as Pb presubscript 82 presuperscript 206 atoms. 

                        (b)     Show that the number of U presubscript 92 presuperscript 238 atoms in the rock sample at time t was 4.0 × 1022.

                        [2]

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                          Key Concepts
                          Half-Life

                          Question 4c

                          Marks: 2

                          The ratio of the number of lead nuclei N subscript P b end subscript to the number of uranium nuclei N subscript U at some time t is given by: 

                          N subscript P b end subscript over N subscript U equals e to the power of lambda t end exponent minus 1

                          λ is the decay constant and has a value of 1.54 × 10−10 years.

                          (c)
                          Calculate the time taken (in years) for there to be twice as many U presubscript 92 presuperscript 238 atoms as Pb presubscript 82 presuperscript 206 atoms.
                          [2]
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                            Key Concepts
                            Decay Curves

                            Question 4d

                            Marks: 4

                            Lead−214 is an unstable isotope of lead−206. It decays by emitting a beta to the power of minus particle to form bismuth−214 (Bi) 

                            Bismuth is also unstable and has two decay modes: 

                            • Emitting an α particle to form thallium−210 (Tl) + energy
                            • Emitting a β particle to form polonium−214 (Po) + energy
                            (d)
                            Write decay equations for the decay chain of lead−214 to thallium−210 and to polonium−214. Comment on the nature of the energy released. 
                            [4]
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                              Key Concepts
                              Decay Equations