![[12%] The ground state wave function for hydrogen atom is (a) N exp(-r/u2) (c) Nr2 exp(-r2/a ) (d) Nexp㈠,21%) (e) N exp(-rlao), where N is the normalized factor and ao is the Bohr radius.](http://img.homeworklib.com/questions/e6443ac0-71df-11ea-84c7-fd8cf6650242.png?x-oss-process=image/resize,w_560)
Homework Answers
Option e is correct as exponential term contains linear power of both r and a because in ground state wavefunction power is always linear as
ψ(r)=(1/π1/2a3/2)e-r/a.
Here this is only available in option e rest all parts contain square of ether r or a or both.
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[12%] The ground state wave function for hydrogen atom is (a) N exp(-r/u2) (c) Nr2 exp(-r2/a...
The wave function for a hydrogen atom in the ground state is given by
( 25 marks) The wave function for a hydrogen atom in the ground state is given by \(\psi(r)=A e^{-r / a_{s}}\), where \(A\) is a constant and \(a_{B}\) is the Bohr radius. (a) Find the constant \(A\). (b) Determine the expectation value of the potential energy for the ground state of hydrogen.
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0...
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0 Where r is the radial coordinate of the electron and a0 is the Bohr radius (a) Show that the wave function as given is normalized (b) Find the probability of locating the electron between rF a0/2 and r2-3ao/2. Note that the following integral may be useful n! 0 dr =-e re /a roa r a Ta
The ground-state wave function of a hydrogen atom is: where r is the distance from the...
The ground-state wave function of a hydrogen atom is:
where r is the distance from the nucleus and a0 is the Bohr
radius (53 pm). Following the Born approximation, calculate the
probability, i.e., |ψ|^2dr, that the electron will be found
somewhere within a small sphere of radius, r0, 1.0 pm centred on
the nucleus.
ρν/α, Ψ1, () =- Μπαρ
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 2s state is
( 25 marks) The normalized wave function for a hydrogen atom in the \(2 s\) state is$$ \psi_{2 s}(r)=\frac{1}{\sqrt{32 \pi a^{3}}}\left(2-\frac{r}{a}\right) e^{-r / 2 a} $$where \(a\) is the Bohr radius. (a) In the Bohr model, the distance between the electron and the nucleus in the \(n=2\) state is exactly \(4 a\). Calculate the probability that an electron in the \(2 s\) state will be found at a distance less than \(4 a\) from the nucleus. (b) At what value...
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
6. The ground state of the hydrogen atom has the form (r)= Ae/a0 where ao is...
6. The ground state of the hydrogen atom has the form (r)= Ae/a0 where ao is the Bohr radius, A is a constant and r is the radial distance of the electron from the nucleus. Find the constant A.
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.
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part...
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
e) A hydrogen atom is in its ground state (n = 1). Using the Bohr theory...
e) A hydrogen atom is in its ground state (n = 1). Using the Bohr theory of the atom, calculate (e) the energy gained by moving to a state where n = 5. g) A hydrogen atom is in its ground state (n = 1). Using the Bohr theory of the atom, calculate (g) the wavelength, λ, of the EM waved adsorbed in the process of moving the electron to a state where n = 5. Hint: There are two...
(1) The ground-state wave function for the electron in a hydrogen is given by ls 0 Where r is the radial coordinate of the electron and a0 is the Bohr radius (a) Show that the wave function as given is normalized (b) Find the probability of locating the electron between rF a0/2 and r2-3ao/2. Note that the following integral may be useful n! 0 dr =-e re /a roa r a Ta
The ground-state wave function of a hydrogen atom is:
where r is the distance from the nucleus and a0 is the Bohr
radius (53 pm). Following the Born approximation, calculate the
probability, i.e., |ψ|^2dr, that the electron will be found
somewhere within a small sphere of radius, r0, 1.0 pm centred on
the nucleus.
ρν/α, Ψ1, () =- Μπαρ
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
6. The ground state of the hydrogen atom has the form (r)= Ae/a0 where ao is the Bohr radius, A is a constant and r is the radial distance of the electron from the nucleus. Find the constant 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.
1) (60 points) The ground state of the hydrogen atom: In three dimensions, the radial part of the Schrodinger equation appropriate for the ground state of the hydrogen atom is given by: ke2 -ħ2 d2 (rR) = E(rR) 2me dr2 where R(r) is a function of r. Here, since we have no angular momentum in the ground state the angular-momentum quantum number /=0. (a) Show that the function R(r) = Ae-Br satisfies the radial Schrodinger equation, and determine the values...
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