Question
(a) Nitrogen-12 \(\left({}^{12}_{7}\mathrm{N}\right)\) is an unstable isotope of nitrogen that decays by the emission of radiation to carbon-12 \(\left({}^{12}_{6}\mathrm{C}\right)\).
Complete the full nuclear equation for the decay, including all the particles involved.
\({}^{12}_{7}\mathrm{N}\rightarrow\) ______________________________ (3 marks)
(b) Hydrogen-1 \(\left({}^{1}_{1}\mathrm{H}\right)\) is an isotope of hydrogen. An atom of hydrogen-1 comprises a proton with an orbiting electron.
An antiparticle equivalent of hydrogen-1 comprises an antiproton with an orbiting positron.
The antiquarks in the antiproton are the antiparticles of the quarks in a proton.
(i) State the charge on the positron in terms of the elementary charge \(e\). (1 mark)
charge = ______________________________ \(e\)
(ii) State the group (class) of fundamental particle to which the positron belongs. (1 mark)
________________________________________________________________________________
(iii) In Table 7.1, state the flavour and charge of the three antiquarks that comprise the antiproton. (3 marks)
Table 7.1
| flavour | charge/\(e\) |
Syllabus Topic Codes (Cambridge International AS & A Level Physics 9702):
• 11.2: Fundamental particles — parts (b)(i), (b)(ii) and (b)(iii)
▶️ Answer/Explanation
(a) Nuclear equation for nitrogen-12 decay [3 marks]
The nucleus changes from nitrogen with proton number \(7\) to carbon with proton number \(6\). Therefore, the proton number decreases by \(1\), indicating \(\beta^+\) decay.
In \(\beta^+\) decay, a positron and a neutrino are emitted.
The complete nuclear equation is
\({}^{12}_{7}\mathrm{N}\rightarrow{}^{12}_{6}\mathrm{C}+{}^{0}_{+1}\mathrm{e}+{}^{0}_{0}\nu\)
Answer: \( \boxed{{}^{12}_{7}\mathrm{N}\rightarrow{}^{12}_{6}\mathrm{C}+{}^{0}_{+1}\mathrm{e}+{}^{0}_{0}\nu} \)
(b)(i) Charge on the positron [1 mark]
A positron is the antiparticle of the electron and has equal magnitude but opposite charge.
Answer: \( \boxed{+1} \)
(b)(ii) Group of fundamental particle [1 mark]
The positron is the antiparticle of the electron. The electron belongs to the lepton group.
Answer: \( \boxed{\text{Lepton}} \)
(b)(iii) Antiquarks in the antiproton [3 marks]
A proton consists of two up quarks and one down quark:
\(p=uud\)
Therefore, an antiproton consists of two anti-up quarks and one anti-down quark:
\(\overline{p}=\overline{u}\,\overline{u}\,\overline{d}\)
| flavour | charge/\(e\) |
| anti-up \(\left(\overline{u}\right)\) | \(-\dfrac{2}{3}\) |
| anti-up \(\left(\overline{u}\right)\) | \(-\dfrac{2}{3}\) |
| anti-down \(\left(\overline{d}\right)\) | \(+\dfrac{1}{3}\) |
Answer: the three antiquarks are two anti-up quarks with charge \(-\dfrac{2}{3}e\) each and one anti-down quark with charge \(+\dfrac{1}{3}e\).