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Chapter 21: Problem 65

Radon-222 decays to a stable nucleus by a series of three alpha emissions and two beta emissions. What is the stable nucleus that is formed?

Short Answer

Expert verified
The stable nucleus formed after Radon-222 undergoes three alpha emissions and two beta emissions is Lead-210 (Pb-210), with 82 protons and 128 neutrons.

Step by step solution

01

Understanding Alpha and Beta Emissions

In an alpha emission, an unstable nucleus loses two protons and two neutrons, resulting in the emission of an alpha particle. In the case of beta emissions, a neutron is converted to a proton, and an electron (beta particle) is released.
02

Identify Radon-222's Protons and Neutrons

Radon has an atomic number of 86, so Radon-222 has 86 protons and 222 - 86 = 136 neutrons.
03

Calculate the changes due to Alpha Emissions

There are three alpha emissions, and in each emission, two protons and two neutrons are lost. So, a total of 6 protons and 6 neutrons are lost. After these emissions, the nucleus has 80 protons (86 - 6) and 130 neutrons (136 - 6).
04

Calculate the changes due to Beta Emissions

There are two beta emissions, and in each emission, a neutron converts into a proton. So, the nucleus gains 2 protons and loses 2 neutrons. The total number of protons becomes 82 (80 + 2) and the number of neutrons becomes 128 (130 - 2).
05

Identify the Stable Nucleus

The stable nucleus formed has 82 protons and 128 neutrons. The element with an atomic number of 82 is lead (Pb). Therefore, the stable nucleus formed is Lead-210 (Pb-210).

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Most popular questions from this chapter

In each of the following pairs, which nuclide would you expect to be the more abundant in nature: (a) \({ }_{48}^{115} \mathrm{Cd}\) or \({ }_{4} 11 \mathrm{Cd}\), (b) \({ }_{13}^{30} \mathrm{Al}\) or \({ }_{13}^{2} \mathrm{Al}\), (c) palladium-106 or palladium113, (d) xenon-128 or cesium-128? Justify your choices.

It takes \(5.2\) minutesfor a \(1.000-g\) sample of \({ }^{210} \mathrm{Fr}\) to decay to \(0.250 \mathrm{~g}\). What is the half-life of \({ }^{210} \mathrm{Fr}\) ?

Charcoal samples from Stonehenge in England were burned in \(\mathrm{O}_{2}\), and the resultant \(\mathrm{CO}_{2}\) gas bubbled into a solution of \(\mathrm{Ca}(\mathrm{OH})_{2}\) (limewater), resulting in the precipitation of \(\mathrm{CaCO}_{3}\). The \(\mathrm{CaCO}_{3}\) was removed by filtration and dried. A \(788-\mathrm{mg}\) sample of the \(\mathrm{CaCO}_{3}\) had a radioactivity of \(1.5 \times 10^{-2}\) Bq due to carbon-14. By comparison, living organisms undergo \(15.3\) disintegrations per minute per gram of carbon. Using the half-life of carbon- 14,5715 yr, calculate the age of the charcoal sample.

Cobalt-60, which undergoes beta decay, has a half-life of \(5.26\) yr. (a) How many beta particles are emitted in \(180 \mathrm{~s}\) by a \(3.75\) -mg sample of \({ }^{60} \mathrm{Co}\) ? (b) What is the activity of the sample in Bq?

Tests on human subjects in Boston in 1965 and 1966 , following the era of atomic bomb testing, revealed average quantities of about \(2 \mathrm{pCi}\) of plutonium radioactivity in the average person. How many disintegrations per second does this level of activity imply? If each alpha particle deposits \(8 \times 10^{-13} \mathrm{~J}\) of energy and if the average person weighs \(75 \mathrm{~kg}\), calculate the number of rads and rems of radiation in \(1 \mathrm{yr}\) from such a level of plutonium.
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