The isotope $^{208} \mathrm{Tl}$ undergoes $\beta$ decay with a half-life of 3.1 min. (a) What isotope is produced by the decay? (b) How long will it take for 99.0$\%$ of a sample of pure $^{208} \mathrm{Tl}$ to decay? (c) What percentage of a sample of pure $^{208} \mathrm{Tl}$ remains un-decayed after 1.0 h?

The equilibrium constant for the reaction$\mathrm{Hg}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) \rightleftharpoons \mathrm{HgCl}_{2}(a q)$ is $1.6 \times 10^{13}$. Is $\mathrm{HgCl}_{2}$ a strong electrolyte or a weak electrolyte? What are the concentrations of $\mathrm{Hg}^{2+}$ and $\mathrm{Cl}^{-}$ in a 0.015-M solution of $\mathrm{HgCl}_{2}$?

In what ways are matter and energy related that were not known before the development of relativity and quantum mechanics?

Name all of the sets of numbers to which each real number belongs. Write whole, integer, rational, or irrational. $-\sqrt{36}$

Solve each equation. Round to the nearest tenth, if necessary. $r^{2}=25,000$

Credit Card Debt John has a balance of $3000 on his Discover card that charges 1% interest per month on any unpaid balance. John can afford to pay$100 toward the balance each month. His balance each month after making a $100 payment is given by the recursively defined sequence$B_{0}=$3000 \quad B_{n}=1.01 B_{n-1}-100$ Determine John's balance after making the first payment. That is, determine $B_{1}$.

(a) Calculate $\gamma$ for a proton that has a momentum of $1.00 \mathrm{kg} \cdot \mathrm{m} / \mathrm{s}.$ (b) What is its speed? Such protons form a rare component of cosmic radiation with uncertain origins.

When 2-ethyl-5-chlorotoluene was treated with sodium hydroxide at high temperature, followed by treatment with $\mathrm{H}_{3} \mathrm{O}^{+}$, three constitutional isomers with the molecular formula $\mathrm{C}_{9} \mathrm{H}_{12} \mathrm{O}$ were obtained. Draw all three products.

the entities in a nuclear reaction that consist of helium atoms are known as?

The isotope $_{38}^{90} \mathrm{Sr}$ is one of the extremely hazardous species in the residues from nuclear power generation. The strontium in a 0.500-g sample diminishes to 0.393 g in 10.0 y. Calculate the half-life.

The thermite reaction, Fe$_2$O$_3$(s) + 2 Al(s) $\longrightarrow$ 2 Fe(s) + Al$_2$O$_3$(s), is one of the most exothermic reactions known. The heat released is sufficient to melt the iron product; consequently, the thermite reaction is used to weld metal under the ocean. $\Delta H^{\circ}$ for the thermite reaction is -851.5 kJ/mole. What is the mass change per mole of Fe$_2$O$_3$ that accompanies this reaction?

One problem with x rays is that they are not sensed. Calculate the temperature increase of a researcher exposed in a few seconds to a nearly fatal accidental dose of x rays under the following conditions. The energy of the x-ray photons is 200 keV, and $4.00 \times 10^{13}$ of them are absorbed per kilogram of tissue, the specific heat of which is $0.830\ \mathrm{kcal} / \mathrm{kg} \cdot^{\circ} \mathrm{C}.$ (Note that medical diagnostic x-ray machines cannot produce an intensity this great.)

One of the compounds from the previous problem has a $p K_{a}<10$. Identify that compound and explain why it is so much more acidic than all of the other compounds.

Consider a battery made from one half-cell that consists of a copper electrode in 1 M $\mathrm{CuSO}_{4}$ solution and another half-cell that consists of a lead electrode in 1 M $\mathrm{Pb}\left(\mathrm{NO}_{3}\right)_{2}$ solution. (a) What are the reactions at the anode, cathode, and the overall reaction? (b) What is the standard cell potential for the battery? (c) Most devices designed to use dry-cell batteries can operate between 1.0 and 1.5 V. Could this cell be used to make a battery that could replace a dry-cell battery? Why or why not. (d) Suppose sulfuric acid is added to the half-cell with the lead electrode and some $\mathrm{PbSO}_{4}(\mathrm{s})$ forms. Would the cell potential increase, decrease, or remain the same?