Problem I. (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect? What is the interval of the frequency in the field B = 0.1 Tesla? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level difference in the unit of [eV] from the value of magnetic dipolar moment of an electron. What is the frequency v of the electro-magnetic wave which can cause transition between the Zeeman levels ? (v) Electron spin in the magnetic field B = 1.0 Tesla undergoes Larmor precession, Obtain the precession frequency by using the relationship between the angular momentum and the torque. (vi) If we put an electric dipole moment in the electric field, shall we expect the similar precession motion? Answer yes or no, and attach a brief reasoning. Please Answer (i)-(vi)
Problem I. (i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits a photon and make a transition to the 2s state. What is the frequency v of this photon ? (ii) Now we do not include electron spin angular momentum, and just estimate an effect of a magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum. How many lines of optical transition do we expect? What is the interval of the frequency in the field B = 0.1 Tesla? (iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the 3s state, Explain the reason. (iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman) levels. Obtain the level difference in the unit of [eV] from the value of magnetic dipolar moment of an electron. What is the frequency v of the electro-magnetic wave which can cause transition between the Zeeman levels ? (v) Electron spin in the magnetic field B = 1.0 Tesla undergoes Larmor precession, Obtain the precession frequency by using the relationship between the angular momentum and the torque. (vi) If we put an electric dipole moment in the electric field, shall we expect the similar precession motion? Answer yes or no, and attach a brief reasoning. Please Answer (i)-(vi)
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Problem I.
(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the
actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits
a photon and make a transition to the 2s state. What is the frequency v of this photon ?
(ii) Now we do not include electron spin angular momentum, and just estimate an effect of a
magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.
How many lines of optical transition do we expect ? What is the interval of the frequency in the
field B = 0.1 Tesla ?
(iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the
3s state, Explain the reason.
(iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a
free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman)
levels. Obtain the level difference in the unit of [eV] from the value of magnetic dipolar
moment of an electron. What is the frequency v of the electro-magnetic wave which can cause
transition between the Zeeman levels ?
(v) Electron spin in the magnetic field B = 1.0 Tesla undergoes Larmor precession, Obtain the
precession frequency by using the relationship between the angular momentum and the torque.
(vi) If we put an electric dipole moment in the electric field, shall we expect the similar precession
motion ? Answer yes or no, and attach a brief reasoning.
Please Answer (i)-(vi)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F9e2ef0db-41f5-441a-b8c0-2b47c5981114%2F86b81088-d730-4586-b5ef-64920d3e7ec9%2Fm5669rs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Physics
Problem I.
(i) Using Bohr model for atomic hydrogen, obtain energy levels for the 2s, 3s and 3p states in the
actual number with the unit of [eV]. We consider a transition that electron in the 3p state emits
a photon and make a transition to the 2s state. What is the frequency v of this photon ?
(ii) Now we do not include electron spin angular momentum, and just estimate an effect of a
magnetic field B on this transition (Normal Zeeman effect) with orbital angular momentum.
How many lines of optical transition do we expect ? What is the interval of the frequency in the
field B = 0.1 Tesla ?
(iii) In this situation, we do not expect transition from 3s to 2s state if the electron is initially in the
3s state, Explain the reason.
(iv) We now consider an effect of magnetic field B to a free electron spin (not in Hydrogen, but a
free electron). The magnetic field of B = 1.0 Tesla will split the energy level into two (Zeeman)
levels. Obtain the level difference in the unit of [eV] from the value of magnetic dipolar
moment of an electron. What is the frequency v of the electro-magnetic wave which can cause
transition between the Zeeman levels ?
(v) Electron spin in the magnetic field B = 1.0 Tesla undergoes Larmor precession, Obtain the
precession frequency by using the relationship between the angular momentum and the torque.
(vi) If we put an electric dipole moment in the electric field, shall we expect the similar precession
motion ? Answer yes or no, and attach a brief reasoning.
Please Answer (i)-(vi)
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