(10 pts) MacIntyre 8.11. Hint: consider the Helium atom as Hydrogen-like with atomic number Z=2. We...
Normalize the wavefunction for a 1s atomic orbital of a hydrogen-like atom with atomic number, Z: , where
An atom with a single electron (i.e. a hydrogen-like atom) has an atomic number Z = 3. What is the principal quantum number of the state in which the electron has the same total energy as a ground state electron has in the hydrogen atom?
The Hamiltonian of the helium atom, under the assumption that the mass of the nucleus is much greater than that of the electrons and ignoring the spin, is of the form: Where are the position and momentum of the electron and is the atomic number of helium. Note that the first four terms are simply the sum of two Hamiltonians corresponding to a hydrogen atom for each electron; while the last term represents the interaction between both electrons. i) Investigate...
A neutral hydrogen atom in its normal state behaves like an electric charge distribution that consists of a point charge of magnitude surrounded by a distribution of negative charge whose density is given by . Here m is the Bohr radius, and is a constant with the value required to make the total amount of negative charge exactly . What is the electric field strength for radius ? What is the electric field strength at radius ? We were unable...
The Bohr model can be applied to singly ionized helium He+ (Z = 2). Using this model, consider the series of lines that is produced when the electron makes a transition from higher energy levels into the = 4 level. Some of the lines in this series lie in the visible region of the spectrum (380−750 nm). What are the values of for the energy levels from which the electron makes the transitions corresponding to these lines? We were unable...
rer Programu In the ammonia (NH3) molecule of the figure, three hydrogen (H) atoms form an equilateral triangle, with the center of the triangle at distance - 9.40 x 10-11 m from each hydrogen atom. The nitrogen (N) atom is at the apex of a pyramid, with the three hydrogen atoms forming the base. The nitrogen-to-hydrogen atomic mass ratio is 13.9, and the nitrogen-to-hydrogen distance is L-10.14 x 10-11 m. What are the (a) x and (b) y coordinates of...
a transition in a hydrogen atom is forbidden if Where r is a vector in cartesian coordinates. Do the radial integral in spherical coordinates for transitions l=0 to l=0 and (l=1,=0) to l=0. show which are forbidden or permitted. We were unable to transcribe this imageWe were unable to transcribe this image
In lab we studied the Bohr model of the hydrogen atom which is verified exactly with quantum mechanical calculations. From quantum mechanics we also find that Bohr’s equation can be used for any one-electron cation like He+, Li2+, Be3+ etc, by including the atomic number, Z, of the cation in the equation with Bohr’s constant (): En= -Z2n2(Accurate for any one-electron cation with atomic number Z) Use this equation to calculate the energy (J) of the first and second energy...
In red giant stars three helium atoms fuse together to form a carbon atom via the process 3()+. A) Calculate the Q value (in Mev) for this reaction (this is the energy in the gamma ray photons and kinetic energy of the carbon nucleus) B) Assuming the Q value represents the mass converted to energy, determine the mass lost in one reaction. C) now using the energy of betelgeuse, determine the mass lost in one reaction. D) how long can...
Suppose that Z is a continuous random variable. Let denote the unnormalized PDF of Z ―the function satisfies all properties of a PDF except that it is not normalized. Now suppose we use to compute something like the moment generating function (MGF), i.e., we compute the function What is ? How can we use to normalize the PDF? b(2) We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable...