1. a 53.8 mg sample of sodium perchlorate contains radioactive chlorine-36 ( who

Question

1. a 53.8 mg sample of sodium perchlorate contains radioactive chlorine-36 ( whose atomic mass is 36.0 amu). If 29.6% of the chlorine atoms in the sample are chlorine-36 and the remainder are naturally occuring nonradioactive chlorine atoms, how many disintegrations per second are produced by this sample? The half life of chlorine-36 is 3.0 x 105 yr.

2. A radioactive decay series that beins with 23290 Th ends with formation of the stable nuclied 20882 Pb. How many alphaparticle emissions and how many beta-particle emissions are involved in the sequence of radioactive decays?

Explanation / Answer

First calculate the number of moles in the sample
Molar mass of NaClO4=23+36+4*16=123g
mass of radioactive NaClO4= 29.6*53.8/100=15.92mg

this corresponds to a number of moles 15.92*10^-3/123=12.9*10^-5m
In atoms of Cl 36 12.9*10^-5*6.022*10^23=7.79*10^19atoms of Cl-36

To calculate number of disintegrations per seconds use the differential formula dN= -N0*t*lambda
where the lambda radioactive constant is lambda =ln2/half-life

lambda = ln2/(3*10^5*365*24*3600)=7.32*10^-14s-1

and result 7.32*10^-14*7.79*10^19=5.7*10^6 Bq (Bq=1desintigration/s)

An alpha decay changes the atomic number by -2 and the atomic mass number by -4 (an alpha particle is a He-4 nucleus containing 2 protons and 2 neutrons).

A beta-minus decay changes the atomic number by +1, and does not change the atomic mass number (a beta-minus particle is an electron).

From the above, it should be clear that only alpha decays change the atomic mass number, so in going from Th-232 to Pb-208, the mass number changes by 232-208 = 24 units. Each alpha decay reduces the mass by 4 units, so there must be 6 alpha decays in this chain.

Each of those alpha decays will change the atomic number by -2, so in the absence of any beta decays, we would end up with a nucleus with atomic number 90 - 2*6 = 78. In fact, Pb has an atomic number of 82, which is 4 units higher than 78. Each beta-minus decay increases the atomic number by 1, so there must be 4 beta decays in this chain.

Related Questions

Navigate

• Browse (All)
• Browse 1
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.