Th232 has a half-life of 14 billion years, it is the longest-lived isotope of thorium. Calculate its decay constant.
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- Unstable nuclei will become stable by radiating energy, this process is called radioactive decay. The rate at which unstable radioactive nuclei decay in a sample of material is called the activity of the sample.
- The decay probability per nucleus per second is called the decay constant it is given by,
Here t1/2 is known as the half-life of the nucleus. It is the time that it takes for the activity to be reduced by half.
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- A radium source contains 1.00 mg of 226Ra, which decays with a half-life of 1600 y to produce 222Rn, a noble gas. This radon isotope in turn decays by alpha emission with a half-life of 3.82 d. If this process continues for a time much longer than the half-life of 222Rn, the 222Rn decay rate reaches a limiting value that matches the rate at which 222Rn is being produced, which is approximately constant because of the relatively long half-life of 226Ra. For the source under this limiting condition, what are (a) the activity of 226Ra, (b) the activity of 222Rn, and (c) the total mass of 222Rn?A 200.0 - mCi sample of a radioactive isotope is purchased by a medical supply house. If the sample has a half - life of 14.0 days, how long will it keep before its activity is reduced to 20.0 mCi?We obviously cannot wait for 4 million years to determine the half-life of technetium, or even 87.7 years to determine the half-life of plutonium. The half-life of a substance is determined using a Geiger counter, which is essentially a tube filled with an inert gas. When a particle decays and produces radiation, it briefly ionizes the gas and produces a detectable electric pulse, which is amplified and counted by a detector (before digital displays were available, you would hear clicks and see a needle register on a dial). Determine the formula for the half-life of a substance, H(M), with an initial count of N0 pulses and a count of N1 pulses M minutes later.
- Americium-243 has a decay constant of 9.39* 10-5 years-1. How long will it take for a sample of americium to lose one-third of its nuclei? please write given, reasoning, and stepsA piece of charcoal used for cooking is found at the remains of an ancient campsite. A 1.19 kg sample of carbon from the wood has an activity of 2340 decays per minute. Find the age of the charcoal. Living mate- rial has an activity of 15 decays/minute per gram of carbon present and the half-life of 14C is 5730 y. Answer in units of y.The half-life of 30P is 2.50 minutes. If a sample of 30P has 1.60 x 1010 nuclei present initially, after 10.0 minutes how many remain?
- 2H is a loosely bound isotope of hydrogen, called deuterium or heavy hydrogen. It is stable but relatively rare — it form only 0.015% of natural hydrogen. Note that deuterium has Z = N, which should tend to make it more tightly bound, but both are odd numbers. Calculate BE/A, the binding energy per nucleon, for 2H in megaelecton volts per nucleon.What fraction f1 of a radioactive sample will be left after 6 half‑lives? What fraction f2 of a radioactive sample will be left after 7.5 half‑lives?Archeologists can determine the age of artifacts made ofwood or bone by measuring the amount of the radioactive iso-tope ¹⁴C present in the object. The amount of isotope decreasesin a first-order process. If 15.5% of the original amount of ¹⁴C is present in a wooden tool at the time of analysis, what is theage of the tool? The half-life of ¹⁴C is 5730 yr.