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1) Write the following wave functions of the Hydrogen atom b100(r, 0, )= 1s b200(r, 0,...
The wave functions for thee 1s and 2s orbitals are as follows 1s 2s 3/2 where...
The wave functions for thee 1s and 2s orbitals are as follows 1s 2s 3/2 where ao is a constant (ao -53 pm) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the difference sin the pots and identify thee node in the 2s wave function (10 pts)
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in...
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
The normalized wave function for a hydrogen atom in the 1s state is given by ψ(r)...
The normalized wave function for a hydrogen atom in the 1s state is given by ψ(r) =( 1 /(\sqrt{\pi a_{0}}) )e^{-r/a_{0}} \) where α0 is the Bohr radius, which is equal to 5.29 × 10-11 m. What is the probability of finding the electron at a distance greater than 7.8 α0 from the proton?
The normalized wave function for a hydrogen atom in the 1s state is given by ψ(r)...
The normalized wave function for a hydrogen atom in the
1s state is given by
ψ(r) = where
α0 is the Bohr radius, which is equal to 5.29 × 10-11 m.
What is the probability of finding the electron at a distance
greater than 7.8 α0 from the proton?
Anwer is 2.3 × 10-5, but how can I get it?
ας παο
ANSWER ALL QUESTIONS 1. (a) The hydrogen atom wave functions are written as Unim. State the...
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...
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...
The ground state wave function of the hydrogen atom is given by 1 (r) = 7/a....
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.
Calculate the expectation value <r> of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the pos...
Calculate the expectation value <r> of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the position from the nucleus. Use the wave functions appropriately in Table 6-1 of the textbook. You can use the integration of x" exp(-ax) dx= a (n>-1, a>0). an+1
Calculate the expectation value of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the position from the nucleus. Use the wave functions appropriately...
The wave functions of the H-atom for the ground state and the first excited state are given by Yo...
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r' exp - , 200(r, θ, φ) a. Show that these 5 wave-functions are all mutually orthogonal to each other. b. Determine the expectation values(r2〉nl of the operator r2 defined as follows 〈r2〉10-rd3TV1,00(a) r2ψ1,0,0(2) and 〈r2〉20, 〈r2)21 defined analogously
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r'...
The wave functions of the H-atom for the ground state and the first excited state are...
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r' exp - , 200(r, θ, φ) a. Show that these 5 wave-functions are all mutually orthogonal to each other. b. Determine the expectation values(r2〉nl of the operator r2 defined as follows 〈r2〉10-rd3TV1,00(a) r2ψ1,0,0(2) and 〈r2〉20, 〈r2)21 defined analogously
The wave functions for thee 1s and 2s orbitals are as follows 1s 2s 3/2 where ao is a constant (ao -53 pm) and r is the distance from the nucleus. Use a spreadsheet to make a plot of each of these wave functions for values of r ranging from 0 pm to 200 pm. Describe the difference sin the pots and identify thee node in the 2s wave function (10 pts)
2. The hydrogen atom [8 marks] The time-independent Schrödinger equation for the hydrogen atom in the spherical coordinate representation is where ao-top- 0.5298 10-10rn is the Bohr radius, and μ is the electon-proton reduced mass. Here, the square of the angular momentum operator L2 in the spherical coordinate representation is given by: 2 (2.2) sin θー sin θ 00 The form of the Schrödinger equation means that all energy eigenstates separate into radial and angular motion, and we can write...
The normalized wave function for a hydrogen atom in the
1s state is given by
ψ(r) = where
α0 is the Bohr radius, which is equal to 5.29 × 10-11 m.
What is the probability of finding the electron at a distance
greater than 7.8 α0 from the proton?
Anwer is 2.3 × 10-5, but how can I get it?
ας παο
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...
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.
Calculate the expectation value <r> of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the position from the nucleus. Use the wave functions appropriately in Table 6-1 of the textbook. You can use the integration of x" exp(-ax) dx= a (n>-1, a>0). an+1
Calculate the expectation value of an electron in the state of n=1 and 1-0 of the hydrogen atom. r is the position from the nucleus. Use the wave functions appropriately...
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r' exp - , 200(r, θ, φ) a. Show that these 5 wave-functions are all mutually orthogonal to each other. b. Determine the expectation values(r2〉nl of the operator r2 defined as follows 〈r2〉10-rd3TV1,00(a) r2ψ1,0,0(2) and 〈r2〉20, 〈r2)21 defined analogously
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r'...
The wave functions of the H-atom for the ground state and the first excited state are given by Yoo(θ, φ), 100(r' exp - , 200(r, θ, φ) a. Show that these 5 wave-functions are all mutually orthogonal to each other. b. Determine the expectation values(r2〉nl of the operator r2 defined as follows 〈r2〉10-rd3TV1,00(a) r2ψ1,0,0(2) and 〈r2〉20, 〈r2)21 defined analogously
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