Write down the partition function for this system. What's the probability of finding the atom in its ground state, if e/kT = In (3)? Assume now that the atom has a second excited state that's 9-fold degenerate and has energy 26. What's the probability of finding the atom with energy E = 2ɛ, again
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- Please do A, B, and C(a) Prove the "vertical angle hypothesis" (I. 15): opposing angles are congruent if two lines cut each other. (Hint: You'll need to use postulate 4 about right angles in this case.) ) (b) Complete the proof of the Exterior Angle Theorem using section (a): illustrate why beta < alphaExample of numerical instability: Take y′ = −5y, y(0) = 1. We know that the solution should decay to zero as x grows. Using Euler’s method, start with h= 1 and compute y1, y2, y3, y4 to try to approximate y(4). What happened? Now halve the interval. Keep halving the interval and approximating y(4) until the numbers you are getting start to stabilize (that is, until they start going towards zero).
- For the ground state electronic configuration of a Si atom. Write out the orbital energy diagram for its ground state. (think Hund’s rule - lowest energy) Use the Clebsch-Gordan series to deduce the term symbols(remember that closed shell and paired up electrons make no net contribution to the spin angular momentum and don’t enter into the term symbol)Ignoring the fine structure splitting, hyperfine structure splitting, etc., such that energy levels depend only on the principal quantum number n, how many distinct states of singly-ionized helium (Z = 2) have energy E= -13.6 eV? Write out all the quantum numbers (n, l, me, ms) describing each distinct state. (Recall that the ground state energy of hydrogen is E₁ = -13.6 eV, and singly-ionized helium may be treated as a hydrogen-like atom.)In the following questions, we will use quantum states made up of the hydrogen energy eigenstates: Q1: Consider the election in a hydrogen atom to initially be in the state: F A. B. C. a) What is the probability of measuring the energy of this state and obtaining E₂? √3 √ vnim (r0,0)=R(r)Y," (0,0) always Y(t = 0) = √3 R₁OYO at t=0 but something different at t>0 ² at t=0 but something different at t>0 D. always 3 + E. Something else. b) Explain your answer. R₂₁ + R32Y₂¹
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- Now consider a system too big for your program to handle: it has a total of 10000 oscillators, with 3000 quanta to be distributed between them. Block 1 has 7000 oscillators, and block 2 has 3000 oscillators. Think about what you observed above. For the most probable distribution of energy between the blocks: How many quanta would you expect to find in block 1? quanta in block 1 How many quanta would you expect to find in block 2? quanta in block 2An electron is confined to a 1-dimensional infinite potential well of dimensions 1.55 nm. Find the energy of the ground state of the electron. Give your answer in units of electron volts (eV). Round your answer to 2 decimal places. Add your answer