Problem 8 (30 pts). The ground state wave function for the hydrogen atom is: W... (7,0,)...
Problem 8 (30 pts). The ground state wave function for the hydrogen atom is: W... (1,0,0) - (a, 15pts) Find (-) for an electron in this state. Find <x> and <p>
4. The wave function for an electron in the ground state of a hydrogen atom is How much more likely is the electron to be at a distance a from the nucleus than at a distance a-/2? Than at a distance 2a ?
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the values of n, I, and m. State the relation between a physical quantity and each quantum number. At =0 the hydrogen atom is in the superposition state (7,0) = 4200 + A¥210 V3 where A is a real positive constant. Find A by normalization and determine the wave function at time t > 0. Find the average energy of the electron in eV given...
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the values of n, I, and m. State the relation between a physical quantity and each quantum number. At =0 the hydrogen atom is in the superposition state (7,0) = 4200 + A¥210 V3 where A is a real positive constant. Find A by normalization and determine the wave function at time t > 0. Find the average energy of the electron in eV given...
( 25 marks) The wave function for a hydrogen atom in the ground state is given by \(\psi(r)=A e^{-r / a_{s}}\), where \(A\) is a constant and \(a_{B}\) is the Bohr radius. (a) Find the constant \(A\). (b) Determine the expectation value of the potential energy for the ground state of hydrogen.
The ground state wave function of the hydrogen atom is given by 1 (r) = 7/a. Vπα3 What is the ground state wave function of the hydrogen atom in momentum space? Hint: Choose the z-axis along the momentum direction.
The ground-state wave function of a hydrogen atom is:
where r is the distance from the nucleus and a0 is the Bohr
radius (53 pm). Following the Born approximation, calculate the
probability, i.e., |ψ|^2dr, that the electron will be found
somewhere within a small sphere of radius, r0, 1.0 pm centred on
the nucleus.
ρν/α, Ψ1, () =- Μπαρ
The vave function for an electron in the ground state of a hydrogen atom is How much more likely is the electron to be at a distance a from the nucleus than at a distance a /2? Than at a distance 2a?
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0 Where r is the radial coordinate of the electron and a0 is the Bohr radius (a) Show that the wave function as given is normalized (b) Find the probability of locating the electron between rF a0/2 and r2-3ao/2. Note that the following integral may be useful n! 0 dr =-e re /a roa r a Ta
8· A hydrogen atom is in its ground state (n = 1). Find the wavelengths of photons it needs to absorb in order to (a) get excited to n-5 or (b) to eject a 10-eV electron.