Erwin Schrödinger Solution of the Schrödinger wave equation for the hydrogen atom results in a set of functio (orbitals) that describe the behavior of the electron. Each function is characterized by 3 quantum numbers: n, I, and m, n is known as the I is known as the m, is known as the n specifies / specifies m, specifies A.The orbital orientation. quantum number. quantum number. quantum number. B.The subshell - orbital shape. C.The energy and average distance from the nucleus.

In 1885, Johann Balmer, a mathematician, derived the following relation for the wavelength of lines in the visible spectrum of hydrogen =364.5 n2( n2 4) where in nanometers and n is an integer that can be 3, 4, 5, . . . Show that this relation follows from the Bohr equation and the equation using the Rydberg constant. Note that in the Balmer series, the electron is returning to the n=2 level.

Calculate the energies of an electron in the fourth, fifth, and sixth energy levels of the Bohr hydrogen atom.

Consider the orbitals shown here in outline. (a) What is the maximum number of electrons contained in an orbital of type (x)? Of type (y)? Of type (z)? (b) How many orbitals of type (x) are found in a shell with n=2? How many of type (y)? How many of type (z)? (c) Write a set of quantum numbers for an electron in an orbital of type (x) in a shell with n=4, of an orbital of type (y) in a shell with n=2. Of an orbital of type (z) in a shell with n=3. (d) What is the smallest possible n value for an orbital of type (x)? Of type (y)? Of type (z)? (e) What are the possible I and ml values for an orbital of type (x)? Of type (y)? Of type (z)?

The helium ion He+ is a one-electron system whose wave functions and energy levels are obtained from those for H by changing the atomic number to Z=2 . Calculate the average distance of the electron from the nucleus in the 2s orbital and in the 2p orbital. Compare your results with those in Problem 11 and explain the difference.

Construct an energy level diagram showing all orbitals for the hydrogen atom up to n=5, labeling each orbital with its appropriate quantum numbers. How many different orbitals are in each shell?

The wave function of an electron in the lowest (that is, ground) state of the hydrogen atom is (r)=( 1 a 0 3 )1/2exp(r a 0 )ao=0.5291010m (a) What is the probability of finding the electron inside a sphere of volume 1.0pm2 , centered at the nucleus (1pm=1012m) ? (b) What is the probability of finding the electron in a volume of 1.0pm2 at a distance of 52.9 pm from the nucleus, in a fixed but arbitrary direction? (c) What is the probability of finding the electron in a spherical shell of 1.0 pm in thickness, at a distance of 52.9 pm from the nucleus?

State how many radial, angular, and total nodes are in each of the following hydrogen-like wavefunctions. a 2s b 3s c 3p d 4f e 6g f 7s

• use Planck’s equation to calculate the energy of a photon from its wavelength or frequency.

A 25-kg child is on a merry-go-round/calliope, going around and around in a large circle that has a radius of 8meters. The child has an angular momentum of 600kgm2/s. a From these facts, estimate the approximate quantum number for the angular momentum the child has. b Estimate the quantized amount of energy the child has in this situation. How does this compare to the childs classical energy? What principle does this illustrate?