Related questions with answers

(a) Using data from the Table, find the mass destroyed when the energy in a barrel of crude oil is released. (b) Given these barrels contain 200 liters and assuming the density of crude oil is $750 \mathrm{kg} / \mathrm{m}^{3},$ what is the ratio of mass destroyed to original mass, $\Delta m / m?$

\begin{array}{|l|l|} \hline {\text { Object/phenomenon }} & \text { Energy in joules } \\ \hline \text { Big Bang } & 10^{68} \\ \hline \text { Energy released in a supernova } & 10^{44} \\ \hline \text { Fusion of all the hydrogen in Earth's oceans } & 10^{34} \\ \hline \text { Annual world energy use } & 4 \times 10^{20} \\ \hline \text { Large fusion bomb (9 megaton) } & 3.8 \times 10^{16} \\ \hline \text { 1 kg hydrogen (fusion to helium) } & 6.4 \times 10^{14} \\ \hline \text { 1 kg uranium (nuclear fission) } & 8.0 \times 10^{13} \\ \hline \text { Hiroshima-size fission bomb (10 kiloton) } & 4.2 \times 10^{13} \\ \hline 90,000 \text { -ton aircraft carrier at 30 knots } & 1.1 \times 10^{10} \\ \hline \text { 1 barrel crude oil } & 5.9 \times 10^{9} \\ \hline 1 \text { ton } \mathrm{TNT} & 4.2 \times 10^{9} \\ \hline 1 \text { gallon of gasoline } & 1.2 \times 10^{8} \\ \hline \text { Daily home electricity use (developed countries) } & 7 \times 10^{7} \\ \hline \text { Daily adult food intake (recommended) } & 1.2 \times 10^{7} \\ \hline 1000-\mathrm{kg} \text { car at } 90 \mathrm{km} / \mathrm{h} & 3.1 \times 10^{5} \\ \hline 1 \mathrm{g} \text { fat }(9.3 \mathrm{kcal}) & 3.9 \times 10^{4} \\ \hline \text { ATP hydrolysis reaction } & 3.2 \times 10^{4} \\ \hline 1 \mathrm{g} \text { carbohydrate }(4.1 \mathrm{kcal}) & 1.7 \times 10^{4} \\ \hline 1 \mathrm{g} \text { protein }(4.1 \mathrm{kcal}) & 1.7 \times 10^{4} \\ \hline \text { Tennis ball at } 100 \mathrm{km} / \mathrm{h} & 22 \\ \hline \text { Mosquito }\left(10^{-2}\ \mathrm{g}\ \mathrm{at} 0.5 \mathrm{m} / \mathrm{s}\right) & 1.3 \times 10^{-6} \\ \hline \text { single electron in a TV tube beam } & 4.0 \times 10^{-15} \\ \hline \text { Energy to break one DNA strand } & 10^{-19} \\ \hline \end{array}

You are working in a laboratory, and you are given the task of converting cyclopentene into 1,5-pentanediol. Your first thought is simply to perform an ozonolysis followed by reduction with $\mathrm{LiAIH}_{4}$ , but your lab is not equipped for an ozonolysis reaction. Suggest an alternative method for converting cyclopentene into 1,5-pentanediol.

What is the approximate uncertainty in the mass of a muon, as determined from its decay lifetime?

Question

A singly ionized helium ion has only one electron and is denoted $\mathrm{He}^{+}.$ What is the ion’s radius in the ground state compared to the Bohr radius of hydrogen atom?

Solution

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$\textbf{Concept: }$

As we know atom is the smallest unit of elements which is combine to form molecules and the molecules are combining to form the matter. Also, we know that the first direct observation of atoms was in brownian motion which give accurate sizes for atoms in range $10^{-10} \mathrm{~m}$ . Also, we know that the atom consists of electrons, protons and neutrons. We know that the charge-to-mass ratios are given by

\begin{align*} \dfrac{q_{e} }{ m_{e} } &= - 1.76 \times 10^{11} \mathrm{~C/kg} \\ \dfrac{ q_{p} }{ m_{p} } &= 9.57 \times 10^{7} \mathrm{~C/kg} \\ \end{align*}

Where, the mass of the electron is $m_{e} = 9.11 \times 10^{-31} \mathrm{~kg}$ and the mass of proton is $m_{p} = 1.67 \times 10^{-27} \mathrm{~kg}$ .