b) An atom has 54 protons, 72 neutrons, and 48 electrons. Write the element, mas
ID: 2019653 • Letter: B
Question
b) An atom has 54 protons, 72 neutrons, and 48 electrons. Write the element, mass number and ionization state.
c) Lead-213 (Pb) decays by -decay with a half-lifr of 10 minutes. Determine the decay products for the decay of lead-213.
d) Which is larger (or are they equal?), the mass of a lead-213 nucleus or the combined mass of it's decay products? Explain.
e) At noon, a sample of lead-213 has an activity of 7.5E-6 Bq. What is the activity of the sample at 12:30?
f) The mass of one atom of lead-213 is 213u. (1u=1.66E-27 kg). If at noon, the sample is pure lead-213, what was the mass of the sample at noon?
a) How many protons, neutrons, and electrons are there in a neutral atom of 80 Br? b) An atom has 54 protons, 72 neutrons, and 48 electrons. Write the element, mass number and ionization state. c) Lead-213 (Pb) decays by ?-decay with a half-lifr of 10 minutes. Determine the decay products for the decay of lead-213. d) Which is larger (or are they equal?), the mass of a lead-213 nucleus or the combined mass of it's decay products? Explain. e) At noon, a sample of lead-213 has an activity of 7.5E-6 Bq. What is the activity of the sample at 12:30? f) The mass of one atom of lead-213 is 213u. (1u=1.66E-27 kg). If at noon, the sample is pure lead-213, what was the mass of the sample at noon?Explanation / Answer
a) 80Br has an atomic number of 35, so it has 35 protons. Since it's neutral, it contains as many electrons as protons, or 35 electrons. Since it has a nucleon number of 80, and a proton number of 35, it has 80 - 35 = 45 neutrons.
b) 54 protons gives us the element of Xe. If it has 54 protons and 72 neutrons, then it has a mass number of 54 + 72 = 126. Since it has 54 protons, each with a +1 charge, and only 48 electrons, each with a -1 charge, then the ionization state of this atom is 54 - 48 = +6, so the atom is
126Xe+6
c) 213Pb ----(-)---> 213Bi + e- + anti-neutrino
A beta decay converts a neutron to a proton, producing an electron and anti-neutrino. So, the element number increaes by one, converting lead to bismuth, but it doesnt change the nucelon number, so it remains 213.
d) Lead-213 has a higher mass. We know from fission (used in nuclear reactors, atomic bombs, etc) that energy is released when you break the bonds of a nucleus, and we know that mass is just anothe form of energy. So the fact that the nucleus has a lot of binding energy increases its mass over the mass of the decay products, which wouldn't have all that binding energy.
e) The half life of lead-213 is 10 minutes, so its decay constant is
= ln(2)/10 minutes = 0.0693 1/min
So, if it's initial acitivty is A(0) = 7.5*10^-6 Bq, then, after 30 minutes,
A(t) = A(0)e^(-t), A(30) = (7.5*10^-6 Bq)e^(-0.0693 * 30) = 9.38*10^-8 Bq
f) A(0) = N(0), so N(0) = A(0)/ = (7.5*10^-6 Bq)/(0.0693 1/min * 1min/60s) = 6.49*10^-3 atoms
Each atom contains 213u, and each u = 1.66*10^-27 kg, so the mass is
m = 6.49*10^-3 atoms * (213u/atom)*(1.66*10^-27 kg/u) = 2.29*10^-27 kg
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