Two electrons in the same atom both have n = 6 and = 1. Assume the electrons are distinguishable, so that interchanging them defines a new state. (a) How many states of the atom are possible considering the quantum numbers these two electrons can have? (b) How many states would be possible if the exclusion principle were inoperative?
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- Two electrons in the same atom have n = 3 and l = 1. (a) List the quantum numbers for the possible states of the atom. (b) How many states would be possible if the exclusion prin- ciple did not apply to the atom?Suppose two electrons in an atom have quantum numbers n = 3 and ℓ = 2. (a) How many states are possible for those two electrons? (Keep in mind that the electrons are indistinguishable.) (b) If the Pauli exclusion did not apply to the electrons, how many states would be possible?Suppose two electrons in an atom have quantum numbers n = 7 and e = 5. (a) How many states are possible for those two electrons? (Keep in mind that the electrons are indistinguishable.) (b) If the Pauli exclusion did not apply to the electrons, how many states would be possible?
- Two electrons in the same atom have n = 3 and ℓ = 1. (a) List the quantum numbers for the possible states of the atom. (b) How many states would be possible if the exclusion principle did not apply to the atom?(a) Make a chart showing all possible sets of quantum numbers l and ml for the states of the electron in the hydrogen atom when n = 4. How many combinations are there? (b) What are the energies of these states?One can now use integrated-circuit technology to manufacture a "box" that traps electrons in a region only a few nanometers wide. Imagine that we make an essentially one-dimensional box with a length of 3 nanometers. Suppose we put 10 electrons in such a box and allow them to settle into the lowest possible energy states consistent with the Pauli exclusion principle. a) What will be the value of the highest energy level occupied by at least one electron? b) What will be the electrons' total energy (ignoring their electrostatic repulsion)? c) How would your answers to the above be different if the electrons were bosons instead of fermions? d) What is the wavelength of the lowest energy photon that can be absorbed (the electrons in this box are fermions)?
- I need to determine if the given state is entangled or not. |ϕ1⟩ = (1 / √3) |00⟩ − (i / √3) |01⟩ + (1+ i / √6) |11⟩An electron (restricted to one dimension) is trapped between two rigid walls 1.26 nm apart. The electron's energy is approximately 24 eV. a) What is the quantum number n for the energy state that the electron occupies? b) Based on the quantum number you found in part (a), calculate a more precise value for the electron's energy (in eV), expressed to at least three significant figures. (Use any physical constants or unit conversions to at least four significant figures in your calculations.)(A) An electron is confined between two impenetrable walls 0.200 nm apart. Determine the energy levels for the states n = 1, 2, and 3.
- (a) Using the Pauli exclusion principle and the rules relating the allowed values of the quantum numbers (n, l, m1, ms) , prove that the maximum number of electrons in a subshell is 2n2 .(b) In a similar manner, prove that the maximum number of electrons in a shell is 2n2In a one-dimensional system, the density of states is given by N(E)= 2m, where L is the length of the sample L√2m in the and m is the mass of the electron, as seen in class. There are N quantum particles with spin |S| = sample (the quantum particles can be understood as 'special electrons with spin [S] ='), so that each state can be occupied by 2|S| + 1 particles. Determine the Fermi energy at 0 K.Soru 6 33492 Thirteen electrons are trapped in a two-dimensional infinite potential well of width L Assume that the electrons do not interact with one another, they follow the Pauli principle and they have spin quantum number. What multiple of gives the energy of the ground state of this system? [Genişliği L olan iki-boyutlu, sonsuz bir potansiyel kuyusunda onüç tane elektron bulunuyor. 8mL Elektronların birbiri ile etkileşmediğini, Pauli prensibine uyduklarını ve bir spin kuantum sayıISına sahil oldklarını farzedelim. Bu sistemin taban enerjisi h2 'nin kaç katıdır?] O a. 13 O b. 9 O c. 10 O d. 5 O e. 8 Sonraki sayfa