Generally, more massive nuclides tend to be more unstable to alpha decay. For example, the most stable isotope of uranium, 238U, has an alpha decay half-life of 4.5 x 10° y. The most stable isotope of plutonium is 244Pu with an 8.0 x 10’ y halflife, and for curium we have 248Cm and 3.4 x 105 y. When half of an original sample of 238U has decayed, what fraction of the original sample of (a) plutonium and (b) curium is left?

The New Horizons spacecraft, launched in 2006, spent 9.5 years on its journey to Pluto. It derives its electric power from the heat generated by 10 kg of 238Pu, which has an activity of 6.3 × 1015 Bq. Each decay emits an alpha particle with an energy of 5.6 MeV. What is the total thermal power generated by this plutonium source?

238U is long-lived but ultimately unstable; it will eventually spontaneously break into two fragments, a 4He nucleus and a 234Th nucleus, in a process called alpha decay, which we’ll learn about in the next section. A great dealof energy is released in the process. What must be true about the masses of the nuclei involved?A. mU > mTh + mHeB. mU = mTh + mHeC. mU < mTh + mHe

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.

A piece of charcoal (totally carbon) from an ancient campsite has a mass of 262 grams.  It is measured to have an activity of 29 Bq from 14C decay.  Use this information to determine the age of the campfire.   Your answer is required to be in years. Information:    14C half-life is 5730 years. 1 gram of living carbon has 6.52x1010 atoms of 14C

Radioactive potassium-40 has a half-life of 4.2 x 1016 s. a) Calculate the decay constant of potassium-40. b) A sample of potassium-40 has an initial mass of 1.0 g. Calculate the number of parent nuclei present in the sample, as well as the initial activity of the source. (One mole of potassium-40 has a mass of 40 g and NA = 6.0 x 1023 mol-1) c) Calculate the number of parent nuclei present in the sample after 9.2 x 1016 s.

Using the data from Table 1, how much energy is released in the fusion of deuterium 12 D and tritium 13T   if helium and a neutron are formed in the reaction? Question 33 options: a 5.98 x 10-10 J b 7.48 x 10-10 J c 1.70 x 1015 J d 2.81 x 10-12 J

E c) For a radio-nuclide, a number No of atoms at time t = 0 decays as N(t) = No e¯‹, where A is the decay constant. i) Derive the relationship between the half-life t₁ and the time constant □ = = 1/λ. ii) The radio-nuclide radium-226 has a half-life of 1600 years. Calculate the activity of one gram of radium in Becquerels. iii) Radium-226 decays to radon-222, known as the daughter product. The amount of a daughter product present will vary with time, Na(t). Sketch two graphs, with appropri- ate axes and labels, to show schematically how N(t) and Na(t) evolve if Na(0) = 0, for the two extreme cases where the daughter product is much more radioactive than the parent (\d >> \) and where the daughter product is much less radioactive than the parent (\a << λ). Given that the half-life of radon-226 is 3.8 days, indicate which graph is relevant and estimate the amount of radon in equilibrium with one mole of radium.

An unknown element X has the following isotopes: ⁶⁴X (49.00% abundant), ⁶⁶X (28.00% abundant), ⁶⁸X (23.00% abundant). What is the average atomic mass in amu of X?

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