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The rate of a reaction is found to triple when the concentration of one reactant is tripled. The order of the reaction with respect to this reactant is:

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4. Start from a trial wavefunction of the form $\phi_{trial} = c_1\phi_1 + c_2\phi_2$ where $c_i$s are the variational parameters and the $\phi_i$ may be complex. a. For this wavefunction, show that the variational principle leads to $E_\phi = \frac{c_1^*c_1H_{11} + c_1^*c_2H_{12} + c_1c_2^*H_{21} + c_2^*c_2H_{22}}{c_1^*c_1S_{11} + c_1^*c_2S_{12} + c_1c_2^*S_{21} + c_2^*c_2S_{22}}$ where $H_{ij} = \int \phi_i^*H\phi_jd\tau = H_{ji}$ and $S_{ij} = \int \phi_i^*\phi_jd\tau = S_{ji}$. b. Now apply the variational principle to find a set of $c_i$s that minimize $E_\phi$ to obtain the following secular equations $(H_{11} - E_\phi S_{11})c_1 + (H_{12} - E_\phi S_{12})c_2 = 0$ and $(H_{21} - E_\phi S_{21})c_1 + (H_{22} - E_\phi S_{22})c_2 = 0$ c. The nontrivial solution of the above equations exist if and only if the determinant $\begin{vmatrix} H_{11} - E_\phi S_{11} & H_{12} - E_\phi S_{12} \\ H_{21} - E_\phi S_{21} & H_{22} - E_\phi S_{22} \end{vmatrix} = 0$ which gives a quadratic equation for $E_\phi$. What is the ground-state energy of $E_\phi$?

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How does sympatric and allopatric speciation occur? Which is more common?

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What is the total equivalent capacitance between the terminals if a 12 micro F capacitor is in parallel to 2 capacitors (4 micro F and 15 micro F) in series? What is the charge on each capacitor and the total energy stored?

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How to solve Convert 36.5386 degress to degress, minutes, and seconds

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Find the domain of the following rational function. $h(x) = \frac{x+3}{x^2 - 9}$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The domain of h(x) is restricted to (Type your answer in interval notation.) B. The domain of h(x) has no restrictions.

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A nurse is caring for a 30-year-old female client who has been diagnosed with uterine leiomyoma. What does the nurse expect to see as the client's presenting chief complaints? a. Feeling of vaginal pressure b. Heavy vaginal bleeding c. Intermittent pain d. Urinary changes

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1. Assume that you are considering going to a trade school for one year to learn how to be a deep-sea diver. The cost of this schooling will be $35,000; given the rigors of this program, you will not be able to work during this year. Assume that you will then be a deep sea diver for only 10 years after that; the reason you can do it for only 10 years is because after that period, your lungs will be so damaged by the pressures of the sea that you won't be able to dive anymore. Your annual income from being a diver will be $50,000. If you don't go to school, you will work at Wal-Mart for the 11 years, earning $20,000 per year. Assume no pay raises. Assume the interest rate is 5%. Should you go to school to be a deep-sea diver? Explain.

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PHY352 HW#3 Consider the $\ell = 2$ states (for some given principal quantum number $n$, which is irrelevant) of the H atom, taking into account the electron spin $1/2$. (a) Enumerate all states in the $J, M$ representation arising from the $\ell = 2$, 1) Two states have $m_j = M = +1/2$. Identify them and write them precisely in terms of the product $Y_\ell^m \chi_\pm$

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1. FIGURE Q1 shows the schematic diagram of a stamping mechanism that is driven by the square link which rotates counter-clockwise. a. D C 85 m 45 m 75° 5 m F E 35 m 25 m B A 50 m FIGURE Q1 Square Draw a scaled kinematic diagram of the mechanism and compute the degree of freedom. [5 marks] b. Determine the stroke of link AB and the stamper. [10 marks] c. Investigate whether the mechanism is a quick-return type. Justify your answer. [5 marks]

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ramon c.