Calculate the probability of an electron in the ground state of the hydrogen atom being inside the region of the proton (radius = 1.2 x 10-15 m).
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Calculate the probability of an electron in the ground state of the hydrogen atom being inside the region of the proton (radius = 1.2 x 10-15 m).
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- Calculate the probability of an electron in the 2s state of the hydrogen atom being inside the region of the proton (radius ≈ 1.2 x 10-15 m). Repeat for a 2p electron.An electron is in a 3p state in the hydrogen atom, given that the expectation value is 12.5a_0 What is the probability of finding the electron within +/- a_0 of your expectation value. (That is, in the range (r − a_0) < r < (r+a_0) where r is the expectation value from above. The answer should be 0.1991.The expectation value,A quantum system is described by a wave function (r) being a superposition of two states with different energies E1 and E2: (x) = c191(r)e iEit/h+ c292(x)e¯iE2t/h. where ci = 2icz and the real functions p1(x) and p2(r) have the following properties: vile)dz = ile)dz = 1, "0 = rp(x)T#(x)l& p1(x)92(x)dx% D0. Calculate: 1. Probabilities of measurement of energies E1 and E2 2. Expectation valuc of cnergy (E)If we neglect interaction between electrons, the ground state energy of the helium atom is E =2 z2((- e2)/(2ao)) = -108.848eV (Z=2). The true (measured) value is – 79.006eV.Calculate the interaction energy e2/r12 supposing that both electrons are in the 1s state and r12 that the spin wave function is anti-symmetric. What E is the ground state energy?Needs Complete typed solution with 100 % accuracy.An electron in a hydrogen atom failing from an excited state (n=7) to a relaxed state has the same wavelength as an electron moving at a speed of 7281 m/s. Determine the relaxed orbit that this electron relaxed to.(a) A quantum dot can be modelled as an electron trapped in a cubic three-dimensional infinite square well. Calculate the wavelength of the electromagnetic radiation emitted when an electron makes a transition from the third lowest energy level, E3, to the lowest energy level, E₁, in such a well. Take the sides of the cubic box to be of length L = 3.2 x 10-8 m and the electron mass to be me = 9.11 x 10-³¹ kg. for each of the E₁ and E3 energy (b) Specify the degree of degeneracy levels, explaining your reasoning.Problem 3. Consider the two example systems from quantum mechanics. First, for a particle in a box of length 1 we have the equation h² d²v 2m dx² EV, with boundary conditions (0) = 0 and (1) = 0. Second, the Quantum Harmonic Oscillator (QHO) V = EV h² d² 2m da² +ka²) 1 +kx² 2 (a) Write down the states for both systems. What are their similarities and differences? (b) Write down the energy eigenvalues for both systems. What are their similarities and differences? (c) Plot the first three states of the QHO along with the potential for the system. (d) Explain why you can observe a particle outside of the "classically allowed region". Hint: you can use any state and compute an integral to determine a probability of a particle being in a given region.