Question

question 1 (1 point)
an atom has 98 protons and 249 nucleons. if it undergoes alpha decay, what are the number of protons and neutrons, respectively, in the daughter nucleus?
100, 245
94, 247
96, 245
100, 249

Explanation:

Step1: Recall alpha decay properties

In alpha decay, an alpha particle (which has 2 protons and 2 neutrons, so 4 nucleons) is emitted. So the number of protons in the daughter nucleus will be the original number of protons minus 2, and the number of nucleons (protons + neutrons) will be the original number of nucleons minus 4.

Original number of protons, \( Z = 98 \)
Original number of nucleons, \( A = 249 \)

Step2: Calculate daughter's protons

Daughter's protons, \( Z' = Z - 2 = 98 - 2 = 96 \)

Step3: Calculate daughter's nucleons

Daughter's nucleons, \( A' = A - 4 = 249 - 4 = 245 \)

Step4: Calculate daughter's neutrons

Neutrons in daughter nucleus, \( N' = A' - Z' = 245 - 96 = 149 \) (But we can also check by original neutrons: original neutrons \( N = A - Z = 249 - 98 = 151 \), after decay, neutrons \( N' = N - 2 = 151 - 2 = 149 \), and \( A' - Z' = 245 - 96 = 149 \), which matches. So the number of protons is 96 and neutrons can be found from nucleons - protons, but we just need to match the options. The option with protons 96 and nucleons 245 (so neutrons 245 - 96 = 149) is 96, 245.

Answer:

96, 245 (the option with "96, 245")