The half-life of radium-226 is 1600 years. Suppose we have a 55 mg sample. Find a function that models the mass m(t) remaining after t years m(t)= How much of the sample will remain after 725 years? m(725)=

A radioactive sample was measured 36.1 years ago. It had an activity of 99075.9 Bq. Today, its activity is 7.1 Bq. What is the decay constant (in years-1) of this substance?

Potassium-argon dating is used to measure the age of rocks formed from cooled lava by determining the fraction of the original 40K remaining in a sample from the ratio of 40K:40Ar. Unusually, potassium-40 decays into both 40Ca (89.1% of the time) and 40Ar (10.9% of the time) with a half-life of 1:248 x 109 years. What is the calculated age of a sample in which the faction of 40K remaining was found to be 0.0043? Is this result physically plausible and why?

The half-life of radon is 3.8 days. Calculate the number of disintegrations per second of 2.5 g of radon (a) 4.6x10 disintegrations/s (b) 1.43x106 disintegrations/s (c) 1.1x10'6 disintegrations/s (d) 7.6x106 disintegrations/s

A radioactive material has a decay constant of λ = 0.0586 yr-1. If it starts out with N0 = 9.03 × 1018 particles, how many (N) will be left after t = 407 years have gone by? Express your answer in scientific notation. (Example: 1.23e4)

Consider a small pot with a copper base. The base has a thickness of 2.0 mm and a diameter of 15 cm. Water in this pot is boiling at 100 °C. Heat transfer rate is estimated at 250,000 J/s. Assume that heat enters the water only from the bottom of the pot through the copper base. Find the temperature of the heating element on which the copper bottom rests. 200 720

One method for determining the age of ancient objects is by radiocarbon dating. Natural processes convert nitrogen to Carbon-14, a radioactive isotope with a half-life of 5730 years. When they are alive, animals assimilate Carbon-14 through the food chain. When an animal dies, it stops replacing its carbon and the amount of Carbon-14 decays exponentially. (a) Suppose the minimum detectable amount is 0.1% of the initial amount. What is the maximum age of a fossil that we could date using Carbon-14? (b) Suppose we wanted to date a fossil that was potentially 70 million years old. A radioactive isotope with what half-life would be required?

The You-Yangs are a series of rocky granite ridges to the south-west of Melbourne, whose rocks contain crystals of titanite. A field student measures 98.27% of the titanite crystals contain the thorium isotope 232Th. If thorium has a half-life of ?1/2 =14 x 109 years, what is the student's estimate of the age of the You-Yangs? (Units: Years)

The half life for the decay of carbon-14 is 5.73* 10^3 years. Suppose the activity due to the radioactive decay of the carbon-14in a tiny sample of an artifact made of wood from an archeological dig is measured to be 3.5*10^3 Bq. The activity in a similar-sized sample of fresh wood is measured to be ×9.6103 Bq. Calculate the age of the artifact. Round your answer to 2 significant digits.

A state-of-the-art proton decay experiment is expected to detect 44% of the proton decays in a body of water. Assuming protons have a lifetime of 1031 years, how many m3 of water would you need in order to see 2 decays per month?  (Assume a "month" is one-twelfth of a year.)