IB Physics SL Theme E: Nuclear and quantum physics questions

Answer: A. $A$ is the nucleon number and $Z$ is the proton number. One additional neutron increases the nucleon number by 1 while leaving the proton number, and therefore the element $X$ unchanged. The notation is ${}^{A+1}_{Z}X$

B: increases the proton number while keeping the nucleon number unchanged. C: decreases the nucleon number, corresponding to one fewer neutron at the same proton number. D: increases both the proton and nucleon numbers, adding a proton as well as a neutron.

Remember: adding a neutron changes $A$ not $Z$

Answer: C. The expected number of decays is the probability of decay per nucleus multiplied by the number of nuclei: $0.20 \times 500 = 100$ nuclei. Because decay is random, this is an expected number, not a guarantee of the exact number that will decay.

A: converts the probability 0.20 to 20% and reports 20 as the number of nuclei, without applying the probability to the sample of 500.
B: uses half the stated probability, 0.10, giving 50 nuclei.
D: calculates the expected number that do not decay, $0.80 \times 500 = 400$ nuclei.
Remember: probability predicts an expected fraction of a sample, not which individual nuclei decay.