Date | May 2022 | Marks available | 3 | Reference code | 22M.2.HL.TZ2.9 |
Level | Higher level | Paper | Paper 2 | Time zone | 2 |
Command term | Show that | Question number | 9 | Adapted from | N/A |
Question
In an experiment a beam of electrons with energy 440 MeV are incident on oxygen-16 (O168) nuclei. The variation with scattering angle of the relative intensity of the scattered electrons is shown.
Identify a property of electrons demonstrated by this experiment.
Show that the energy E of each electron in the beam is about 7 × 10−11 J.
The de Broglie wavelength for an electron is given by hcE. Show that the diameter of an oxygen-16 nucleus is about 4 fm.
Estimate, using the result in (a)(iii), the volume of a tin-118 (Sn11850) nucleus. State your answer to an appropriate number of significant figures.
Markscheme
wave properties ✓
Accept reference to diffraction or interference.
440 x 106 x 1.6 x 10-19 OR 7.0 × 10-11 «J» ✓
6.63×10-34×3×1087×10-11 OR 1.24×10-6440×106 OR 2.8 × 10-15 «m» seen ✓
read off graph as 46° ✓
«Use of D=λsinθ=» 3.9 × 10-15 m ✓
Accept an angle between 45 and 47 degrees.
Allow ECF from MP2
ALTERNATIVE 1
use of R∝A13 OR V∝A ✓
volume of Sn=43π(ASnAO)r 3O or equivalent working ✓
2.3 to 2.5 × 10-43 «m3»✓
answer to 1 or 2sf ✓
ALTERNATIVE 2
use of R=Ro×A13 ✓
volume of Sn=43πR3 OR 5.9 x 10-15 seen ✓
8.5 × 10-43 «m3»✓
answer to 1 or 2sf ✓
Although the question expects candidates to work from the oxygen radius found, allow ALT 2 working from the Fermi radius.
MP4 is for any answer stated to 1 or 2 significant figures.
Examiners report
ai) Well answered.
aii) Well answered.
aiii) This was generally well done but quite a few attempted the small angle approximation. Probably worth a mention in the report.
b) Most gained credit from the first alternative solution, trying to use the data as the question intended. There were the inevitable slips and calculator mistakes. Most got the fourth mark.