*SxPauli spin matrices= 1/2 (1₂6). s, = 2/2 (1₂5).SyS₂ = 1/2 (19)0Radia wavefunctions of hydrogen R20 = -3/2² (1-1) exp(-r/2a)R21 1= a-3/2/2 exp (-r/2a)√24Some spherical harmonics1/2x=(-)¹²3 1/2Y₁ = (2²) ¹2² c cosY₁¹ = F3-)1/² sin (871.(a) The radial wavefunction for the ground state of hydrogen is given asR₁(r) = Co exp(-r/ag), where a = 0.53 Å is a Bohr radius. (a) Normalize the aboveавfunction. (b) What is the most probable value of r? (c) What is the expectation value (r)?Betio

Answered: Image /qna-images/answer/64421b7b-de5b-487d-9575-7bd9ff6dd81e.jpg

Answered: 1. (a) The radial wavefunction for the…

Similar questions

[QUANTUM PHYSICS]
The wave function for hydrogen in the 1s state may be expressed as Psi(r) = Ae−r/a0. Determine the most probable value for the location of the electron when the atom is in this state. (Use the following as necessary: A, a0) where A = 1/sqrt(pi*a03)
The wave function ψ(x) = Bxe-(mω/2h)x2is a solution to the simple harmonic oscillator problem. (a) Find the energy of this state. (b) At what position are you least likely to find the particle? (c) At what positions are you most likely to find the particle? (d) Determine the value of B required to normalize the wave function. (e) What If? Determine the classical probability of finding the particle in an interval of small length δ centered at the position x = 2(h/mω)1/2. (f) What is the actual probability of finding the particle in this interval?
Taking the n=3 states as a representative example, explain the relationship between the complexity of hydrogen’s standing waves in the radial direction and their complexity in the angular direction at a given value of n. What relationship would this be considered a direct relationship or inverse relationship?
The expectation value,
Problem 3: Calculate the energy changes corresponding to the transitions of the hydrogen atom. Give all your answers in eV. Part (a) From n = 3 to n = 4. Part (b) From n = 2 to n = 1. Part (c) From n = 3 to n = ∞.
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.
. (1) Find the kinetic, potential and total energies of the hydrogen atorn in the 2nd excited level.
(d) The following orbital belongs to the 3d subshell of the Hydrogen atom: r Y(r, 0, 0) = A(Z) θ, φ) 2 r e 3ao sin² (0) e²i зао where A and ao are constants. Using the operator for the z-component of orbital angular momentum (L₂ = -ih d/do) determine the m, for this particular orbital. (e) Consider the wavefunction, r r Y(r,0,0) = A-e 2do cos(0) do (i) Identify the radial part of this orbital function and the number of radial nodes. (ii) Identify the angular part of the orbital function and the number of angular nodes. Z (iii) Using this information and the L₂ = -ih d/do operator obtain the n, 1, and, m quantum numbers and identify the orbital.
The wave function for the ground state of hydrogen is given by 100(0,0) = Ae¯¯r/ª Find the constant A that will normalize this wave func- tion over all space.
An electron in a hydrogen atom is approximated by a one-dimensional infinite square well potential. The normalised wavefunction of an electron in a stationary state is defined as *(x) = √√ sin (""). L where n is the principal quantum number and L is the width of the potential. The width of the potential is L = 1 x 10-¹0 m. (a) Explain the meaning of the term normalised wavefunction and why normalisation is important. (b) Use the wavefunction defined above with n = 2 to determine the probability that an electron in the first excited state will be found in the range between x = 0 and x = 1 × 10-¹¹ m. Use an appropriate trigonometric identity to simplify your calculation. (c) Use the time-independent Schrödinger Equation and the wavefunction defined above to find the energies of the first two stationary states. You may assume that the electron is trapped in a potential defined as V(x) = 0 for 0≤x≤L ∞ for elsewhere.
Explain each step

1. (a) The radial wavefunction for the ground state of hydrogen is given as Co R₁(r) = o exp(-¹/a₂), where a = 0.53 Å is a Bohr radius. (a) Normalize the above ав function. (b) What is the most probable value of r? (c) What is the expectation value (r)?