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WEEK 3 Notes and Tips The regions or spaces around the nucleus where the probability of finding an electron is zero are called nodes The wavefunction is the product of a radial and an angular component In a one electron atom the electron is defined by the wave s distance from the nucleus and its angle with respect to the x y and z axes The radial contribution Rn l r defines how the wavefunction depends on the distance of the electron from the nucleus the angular contribution Yl ml describes the wavefunction s n l ml Rn l r Yl ml shape Mathematically there is a node whenever our wavefunction equals 0 so we ll have two types of nodes 1 radial and 2 angular Radial nodes are the spherical surfaces around the nucleus where the probability of finding an electron is zero Angular nodes are the planes or planar areas around the nucleus where the probability of finding an electron is zero The square of the wavefunction is proportional to the probability of finding a particle electron at some point in space Squaring the radial component describes the probability of locating the electron at some distance r away from the nucleus Squaring the angular component gives angular probability density which describes the orbital shape To extend the wavefunction to three dimensions we need to use a total of three quantum numbers n l m to describe an atomic orbital the region in space where the electron is located Quantum Number Name principle Values 0 1 2 3 integers main energy level Notes n l angular momentum 0 1 n 1 m or ml magnetic ms spin l l 1 2 subshell type shape of orbital 0 s 1 p 2 d 3 f specific orbital in a sublevel spin of the electron only have two electrons per orbital If we know how many nodes we have we can figure out what atomic orbital we re dealing with If we know what atomic orbital we re dealing with we can figure out how many nodes we have a total of orbital nodes n 1 b of angular nodes l c of radial nodes n l 1 1 The three H atom orbital pictures below represent different states The maps above show where we might find an electron in three dimensional space for a specific atomic orbital White space indicates a node we won t find an electron in those areas i How many angular node s does each of them have 0 1 2 ii How many radial node s does each of them have 2 0 0 iii Identify the orbitals above The first orbital has 2 radial nodes and 0 angular nodes With 2 total nodes its principal energy level is n 3 2 1 Because it has 0 angular nodes l 0 which corresponds to the s orbital It is a 3s orbital The second has 0 radial nodes and 1 angular node With 1 total node its principal energy level is n 2 1 1 Because it has 1 angular node l 1 which corresponds to the p orbital It is a 2p orbital The third has 0 radial nodes and 2 angular nodes With 2 total nodes its principal energy level is n 3 2 1 Because it has 2 angular nodes l 2 which corresponds to the d orbital It is a 3d orbital Bohr s model of the atom said that the atom consisted of a central nucleus containing protons and neutrons with the electrons in circular orbits at specific distances from the nucleus These can be thought of as electron shells with our energy level n An electron normally exists in the lowest energy shell available closest to the nucleus Energy absorbed from a photon can move the electron to a higher energy shell but it will be more unstable it will return to its ground state and emit this energy Bohr used the following equations to describe properties of the hydrogen atom Remember these are only applicable to one electron situations For example the C atom would normally have 6 electrons but the C5 is a carbon ion with one electron quantized energy of specific level n energy absorbed or emitted between energy levels radius of a specific orbit Rh 2 179 x 10 18 J a0 Bohr radius 52 9 pm Z atomic number of element 2 Consider the Bohr model for C5 See answer key in Bruinlearn iii Calculate the amount of energy needed to move the electron infinitely away from the n 2 orbit TIP This question is asking about the ionization energy of this electron when it starts at energy level 2 This is the quantity of energy that the electron in its current state must absorb to be discharged Because it is moving very far away from the initial orbit we can consider the final orbit n infinity 3 i How many 2p orbitals are there in the hydrogen atom How many 3d and 7f orbitals are there To figure out how many specific orbitals we have in a certain subshell s p d f we need to look at quantum number ml For any p orbital l 1 so ml could equal 1 0 or 1 This means that there are three 2p orbitals For any d orbital l 2 so ml could equal 2 1 0 1 or 2 This means that there are five 3d orbitals For any f orbital l 3 so ml could equal 3 2 1 0 1 2 or 3 This means that there are seven 3f orbitals 2p ii Which of the following combinations of quantum numbers are legitimate 3d a n 3 l 3 ml 2 ms 1 2 Illegitimate If n 3 then l can only be 0 1 or 2 b n 3 l 1 ml 2 ms 1 2 Illegitimate If l 1 then ml can only be 1 0 or 1 c n 4 l 2 ml 1 ms 0 Illegitimate ms can only be 1 2 or 1 2 d n 2 l 1 ml 0 ms 1 2 Legitimate iii Write the set of quantum numbers for a 4f orbital n 4 energy level l 3 f orbital shape ml 3 2 1 0 1 2 3 7 specific orbitals ms 1 2 1 2 iv How many angular nodes are there for a 5f orbital How many radial nodes are there for a 4d orbital For a 5f orbital l 3 so it has 3 angular nodes For a 4d orbital there are 4 1 3 nodes total l 2 so 2 nodes are angular and there is 1 radial node In energy level 12 there are n2 144 orbitals total v How many orbitals have n 12 4 Suppose we shine light of wavelength 350nm on an unknown metal surface the maximum kinetic energy of the ejected electrons is 1 5eV Calculate this metal s work function If we shine light an unknown frequency on the same surface the maximum velocity of ejected electrons is 2 4 105 m s calculate the frequency and wavelength of this light …

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