Homework Answers
- Initially the H atom is in its ground state or s-state
(n=1,l=0), written as
state
in the Dirac notation, 
. - An external electric field is applied,
, thus
behaving like a perturbation that is time dependent and we name it
as 
(from s to
p state) - Due to the perturbation, the atom is now in the 2p state
(n=2,l=1) written as
and we
have to find the probabilty that it remains here at time t >>
or as t 
state
in the Dirac notation, 
.
, thus
behaving like a perturbation that is time dependent and we name it
as 
(from s to
p state)
and we
have to find the probabilty that it remains here at time t >>
or as t 
Transition coefficient, 
= 
Since 
has no dependence
within the the integral, it is evaluated as 
Evaluating each of the integrals separately,
(Using the identity 
)
Solving the next integral,
We still have the time integral left, so let's go ahead and solve that too.
The Transmission coefficent is,
Probability = 
For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emi...
For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emission of a photon with an energy of 16.2x10-19 J. For a Ni atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 1.66 A. What is the energy difference between these states in nickel? The energy difference between these states in nickel is the corresponding energy difference for hydrogen The energy difference between these states...
For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emi...
options for 2 and 3 are <,>, or =
For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emission of a photon with an energy of 16.2x1019 J. For a Ga atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 1.34 A. What is the energy difference between these states in gallium? The energy difference between these states in gallium is v the corresponding...
Q2 Assume that an hydrogen atorn is in the ground state atに00. A pulsed electric field...
Q2 Assume that an hydrogen atorn is in the ground state atに00. A pulsed electric field in z-direction єегр( t2/T2) is applied until t- oo. // Show that the total probability of the atom ending up in the n 2 state is, to the first order, is: where w = (E2-E)/h, and a is the Bohr radius.
1) A hydrogen atom, initially in the ground state, is placed in a time-dependent electric field...
1) A hydrogen atom, initially in the ground state, is placed in a time-dependent electric field that turns on suddenly at t 0 E(t) Eo exp(-yt) e t>0 Use first order time-dependent perturbation theory to find the probability that the hydrogen atom will be found in the n 2 level for t (You will need to consider transitions to each of the (1, m) substates separately; use the Wigner-Eckart theorem to help you decide which matrix elements you need to...
For the hydrogen atom, the transition from the 2p state to the is state is accompanied...
For the hydrogen atom, the transition from the 2p state to the is state is accompanied by the emission of a photon with an energy of 16.2x10-19 J. For a Cl atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 4.73 A. What is the energy difference between these states in chlorine? The energy difference between these states in chlorine is the corresponding energy difference for hydrogen. The energy difference between these states...
Compute the change in energy of the 2p→ 1s photon when a hydrogen atom is placed...
Compute the change in energy of the 2p→ 1s photon when a hydrogen atom is placed in a magnetic field of 2.00 T. 2 III. (12pts) The electron of a hydrogen atom is excited to the n= 5 state. (a) what is the Bohr radius of the electron? (b) what is the total energy of the electron? (c) what is the electron’s Coulomb potential energy and kinetic energy? IV. (12pts) X-ray photons of wavelength 0.120 nm are incident on a...
An electron in a Hydrogen atom is in a state with orbital angular momentum 2 (a)...
An electron in a Hydrogen atom is in a state with orbital angular momentum 2 (a) Using the general raising and lowering operator formalism e.g Construct the linear combinations of mi ms states which have 2) j 5/2,my 3/2 3) j-3/2, m,-3/2 (b) An external magnetic field B is applied in the z-direction. The interaction between the external field and the magnetic moment of the electron is given by Hmag_ 2mc Find the energy splitting induced between the states (1)...
An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use ...
An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use your futuristic dual electric/magnetic field tester on the electromagnetic wave to find the directions of the electric field and magnetic field. Your device tells you that the electric field is pointing in the positive y direction and the magnetic field is pointing in the positive z direction. In which direction does the released electromagnetic wave travel? O +x direction O -x direction O ty...
An excited hydrogen atom releases an electromagnetic wave to return to its normal state.
An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use your futuristic dual electric/magnetic field tester on the electromagnetic wave to find the directions of the electric field and magnetic field. Your device tells you that the electric field is pointing in the negative x direction and the magnetic field is pointing in the positive y direction. In which direction does the released electromagnetic wave travel?+x direction-x direction+y direction-y direction+z direction-z direction
An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use...
An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use your futuristic dual electric/magnetic field tester on the electromagnetic wave to find the directions of the electric field and magnetic field. Your device tells you that the electric field is pointing in the positive xdirection and the magnetic field is pointing in the positive z direction. In which direction does the released electromagnetic wave travel?
For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emission of a photon with an energy of 16.2x10-19 J. For a Ni atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 1.66 A. What is the energy difference between these states in nickel? The energy difference between these states in nickel is the corresponding energy difference for hydrogen The energy difference between these states...
options for 2 and 3 are <,>, or =
For the hydrogen atom, the transition from the 2p state to the 1s state is accompanied by the emission of a photon with an energy of 16.2x1019 J. For a Ga atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 1.34 A. What is the energy difference between these states in gallium? The energy difference between these states in gallium is v the corresponding...
Q2 Assume that an hydrogen atorn is in the ground state atに00. A pulsed electric field in z-direction єегр( t2/T2) is applied until t- oo. // Show that the total probability of the atom ending up in the n 2 state is, to the first order, is: where w = (E2-E)/h, and a is the Bohr radius.
1) A hydrogen atom, initially in the ground state, is placed in a time-dependent electric field that turns on suddenly at t 0 E(t) Eo exp(-yt) e t>0 Use first order time-dependent perturbation theory to find the probability that the hydrogen atom will be found in the n 2 level for t (You will need to consider transitions to each of the (1, m) substates separately; use the Wigner-Eckart theorem to help you decide which matrix elements you need to...
For the hydrogen atom, the transition from the 2p state to the is state is accompanied by the emission of a photon with an energy of 16.2x10-19 J. For a Cl atom, the same transition (2p to 1s) is accompanied by the emission of x-rays of wavelength 4.73 A. What is the energy difference between these states in chlorine? The energy difference between these states in chlorine is the corresponding energy difference for hydrogen. The energy difference between these states...
An electron in a Hydrogen atom is in a state with orbital angular momentum 2 (a) Using the general raising and lowering operator formalism e.g Construct the linear combinations of mi ms states which have 2) j 5/2,my 3/2 3) j-3/2, m,-3/2 (b) An external magnetic field B is applied in the z-direction. The interaction between the external field and the magnetic moment of the electron is given by Hmag_ 2mc Find the energy splitting induced between the states (1)...
An excited hydrogen atom releases an electromagnetic wave to return to its normal state. You use your futuristic dual electric/magnetic field tester on the electromagnetic wave to find the directions of the electric field and magnetic field. Your device tells you that the electric field is pointing in the positive y direction and the magnetic field is pointing in the positive z direction. In which direction does the released electromagnetic wave travel? O +x direction O -x direction O ty...
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