C.)1.05 b). a). (e) Plot the potential energy function from 50 pm to 800 pm. 1.00794 + 18.9984032, Note that all formulas are case-sensitive. We can use the same procedure in Q1. \[R_H=\dfrac{me^4}{8\epsilon_o^2 ch^3} \nonumber \], \[R_H=\dfrac{(9.104431 \times 10^{-31}kg)(1.602 \times 10^{-19} C)^4}{8(8.854 \times 10^{-12} \dfrac{F}{m})^2(2.998 \times 10^{8} \dfrac{m}{s})(6.626 \times 10^{-34} J \cdot s)^3} \nonumber \]. In chemistry, the formula weight is a quantity computed by multiplying the atomic weight (in atomic mass units) of each element in a chemical formula by the number of atoms of that element present in the formula, then adding all of these products together. In the absence of a specified axis, we are free to choose any axis. Formula weights are especially useful in determining the relative weights of reagents and products in a chemical reaction. Therefore we have \(B(I_a) = B(I_b)\dfrac{I_b}{I_a}\). correspond to? • μ, reduced mass: m. A m B /(m A +m B ) • N A , Avogadro’s Constant. Each 10% decrease in estimated waist circumference over 1 year was associated with a significant 23% decrease in HF risk, and similar associations were observed for 4-year changes in body composition and HF risk. Hg): medwireNews: The risk for heart failure (HF) falls significantly with reductions in fat mass and waist circumference in overweight or obese people with type 2 diabetes, shows an analysis of data from the Look AHEAD trial. We can calculate \(I_{DCl}\) via the ratio of reduced masses: \[\dfrac{I_{HCl}}{I_{DCl}} = \dfrac{\mu_{HCl}}{\mu_{DCl}}\]. Have questions or comments? The equation for a reduced mass (\(\mu\)) of a diatomic is, \[ \mu= \dfrac{m_1m_2}{m_1+m_2} \nonumber \], for a diatomic molecule with identical atoms (\(m_1=m_2=m\)) so. Find the reduced mass of HCl where the mass of hydrogen in 1 amu and the mass of chloride is 35 amu. \(J\) is the angular momentum quantum number that describes amount of angular momentum the molecule has. The rotational constants for DCl are likely to scale with the difference in moment of inertia. Finding molar mass starts with units of grams per mole (g/mol). \[\dfrac{109707.3\; cm^{-1}}{109677.5\; cm^{-1}}=1.000272 \nonumber \], \[R_H=\dfrac{(9.106909 \times 10^{-31}kg)(1.602 \times 10^{-19} C)^4}{8(8.854 \times 10^{-12} \dfrac{F}{m})^2(2.998 \times 10^{8} \dfrac{m}{s})(6.626 \times 10^{-34} J \cdot s)^3} \nonumber \]. Unless otherwise noted, LibreTexts content is licensed by CC BY-NC-SA 3.0. We use the most common isotopes. We also acknowledge previous National Science Foundation support under grant numbers 1246120, 1525057, and 1413739. Determine the unnormalized wave function \(\psi_\circ \big(x\big)\) given that \(\hat{a}_- = 2^{-1/2}\big(\hat{x}+i\hat{p}\big) \) and that \(\hat{a_-}\psi_\circ = 0\) Then find the unnormalized wave function for \(\psi_1\big(x\big)\) using \(\hat{a}_+\). Q: Which of the following species are isoelectronic with Ne. World DIabetes Day 2020 imagery/© International Diabetes Federation, This site is intended for healthcare professionals only, Targeting fat mass, central adiposity may reduce HF risk in type 2 diabetes | diabetes.medicinematters.com. Type it in sub & super do not work (e. g. H2O) Choose one or more. The formula weight is simply the weight in atomic mass units of all the atoms in a given formula. Molar mass of HF = 20.0063432 g/mol. Learn more about the 2020 World Diabetes Day theme. For negative eigenvalues, we calculate using the absolute value of , then multiply by -1 to make the frequency negative (which flags it as imaginary). e.g. molar mass and molecular weight. Using the resulting value of B, we can find the bond length finding the reduced mass of HF and using it in the expression: \[R = \sqrt{\dfrac{h}{8 \pi^2 \mu B}}\] Q5. Then using the reduced mass calculated find the Rydberg constant for a deuterium atom. A) ... A: Electron density is the particular area where probability of of electrons is maximum. Convert grams HF to moles or moles HF to grams. Significance of the value. Then find the value of the Rydberg constant for the Tritium atom. The reduced mass mu of a system of two bodies with masses m1 and m2 is determined as 1/mu=1/m1+1/m2. c) What is the smallest amount of energy that can be absorbed for a They report in Circulation that each 10% decrease in estimated fat mass over 1 year was associated with a significant 20% decrease in the risk for HF, after adjustment for demographics, treatment assignment, cardiorespiratory fitness, and cardiovascular risk factors. Answer: (a) The harmonic force constantis calculatedfromthe relationship ω= 1 c µ kh µ ¶1/2 orν0(cm−1)= 1 2πc µ kh µ ¶1/2. common chemical compounds. Molecular weight calculation: 1.00794 + 18.9984032 ›› Percent composition by element mu= (Ma*Mb)/ (Ma+Mb) where Ma is the molar mass of element A. so for diatomic Hydrogen H-H both masses are the same, so our equation becomes. First calculate the reduce mass of the deuterium atom. Prove that the second derivative of an even function is even and odd function is odd. Given that the values for \(l\) and \(m\) are the same as above, the answers would also be the same. The Harmonic oscillator Hamiltonian obeys the reflective property: What does this say about the nature of the harmonic oscillator wave function? Solutions to select questions can be found online. This is not the same as molecular mass, which is the mass of a single molecule of well-defined isotopes. b) Compute the moment of inertia of HF (you’ll need to look up the Targeting fat mass, central adiposity may reduce HF risk in type 2 diabetes | diabetes.medicinematters.com The function does not depend on \(\theta\) or \(\phi\) so when the angular momentum operator is applied to the function, it equals 0. b) \(Y(\theta,\phi) = 3\pi \sin(\theta) \), \[\hat{L_x}(3\pi \sin(\theta)) = i\hbar\Big(\sin(\phi)\dfrac{\partial}{\partial \theta}3\pi \sin(\theta) + \cot(\theta)\cos(\phi)\dfrac{\partial}{\partial \phi}3\pi \sin(\theta)\Big) \nonumber \], \[ = 3i\pi\hbar \sin(\phi)\cos(\theta) \nonumber \], c) \(Y(\theta,\phi) = \dfrac{3}{2}\cos(\theta)exp(i\phi)\), \[\hat{L_x}(3\pi \sin(\theta)) = i\hbar\Big(\sin(\phi)\dfrac{\partial}{\partial \theta}\dfrac{3}{2}\cos(\theta)exp(i\phi) + \cot(\theta)\cos(\phi)\dfrac{\partial}{\partial \phi}\dfrac{3}{2}\cos(\theta)exp(i\phi)\Big) \nonumber \], \[ = i\hbar\Big( \dfrac{-3}{2}\sin(\phi)\sin(\theta)exp(i\phi) + \dfrac{3i}{2}\cot(\theta)\cos(\phi)\cos(\theta)exp(i\phi)\Big) \nonumber \], \[ = \dfrac{3i\hbar exp(i\phi)}{2}(i\cot(\theta)\cos(\phi)\cos(\theta) - \sin(\phi)\sin(\theta)) \nonumber \], Use the fact that \(\hat x\) and \(\hat p\) are Hermitian in the number operator, \[ \hat a_- = \dfrac{1}{\sqrt{2}}(\hat x +i\hat p) \nonumber \], \[\hat a_+ = \dfrac{1}{\sqrt{2}}(\hat x -i\hat p) \nonumber \], \[\hat H=\dfrac{\hbar w}{2}(\hat a_-\hat a_+ + \hat a_+\hat a_-) \nonumber \], \[\int \psi^*_v \hat{v} \psi dx \geq 0 \nonumber \].

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