Exotic Atoms
About points...
We associate a certain number of points with each exercise.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
When you click an exercise into a collection, this number will be taken as points for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit the number of points for the exercise in the collection independently, without any effect on "points by default" as represented by the number here.
That being said... How many "default points" should you associate with an exercise upon creation?
As with difficulty, there is no straight forward and generally accepted way.
But as a guideline, we tend to give as many points by default as there are mathematical steps to do in the exercise.
Again, very vague... But the number should kind of represent the "work" required.
About difficulty...
We associate a certain difficulty with each exercise.
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
When you click an exercise into a collection, this number will be taken as difficulty for the exercise, kind of "by default".
But once the exercise is on the collection, you can edit its difficulty in the collection independently, without any effect on the "difficulty by default" here.
Why we use chess pieces? Well... we like chess, we like playing around with \(\LaTeX\)-fonts, we wanted symbols that need less space than six stars in a table-column... But in your layouts, you are of course free to indicate the difficulty of the exercise the way you want.
That being said... How "difficult" is an exercise? It depends on many factors, like what was being taught etc.
In physics exercises, we try to follow this pattern:
Level 1 - One formula (one you would find in a reference book) is enough to solve the exercise. Example exercise
Level 2 - Two formulas are needed, it's possible to compute an "in-between" solution, i.e. no algebraic equation needed. Example exercise
Level 3 - "Chain-computations" like on level 2, but 3+ calculations. Still, no equations, i.e. you are not forced to solve it in an algebraic manner. Example exercise
Level 4 - Exercise needs to be solved by algebraic equations, not possible to calculate numerical "in-between" results. Example exercise
Level 5 -
Level 6 -
Question
Solution
Short
Video
\(\LaTeX\)
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Exercise:
To test the validity of the quantum mechanical description of the hydrogen atom the energy levels of various exotic atoms have been investigated. The experimental results agree with the theoretical predictions. vspacemm Calculate the first energy level for abcliste abc a muonic hydrogen atom i.e. a hydrogen atom where the electron is replaced by a muon m_mummuO. abc a muonic lead atom. abc positronium a configuration of a positron anti-electron and an electron. Since the two masses are identical the reduced mass mum_e/ has to be used instead of the electron mass. abcliste
Solution:
The energy of the ground state of an electron in the potential of a nucleus with charge Ze is given by E_ -fracZ^ e^ m_eepsilon_^ h^ When the electron is replaced by another particle with charge -e the mass has to be adjusted accordingly. abcliste abc The energy can be calculated as E_ -fracZ^ e^ m_muepsilon_^ h^ -fracZ^ e^ m_eepsilon_^ h^fracm_mum_eE_efracm_mum_e where E_eEgrO is the energy of the ground state of the regular hydrogen atom. It follows for the myonic hydrogen atom E_mu Egrtimesfracmmume resultEHmuP abc For a muonic lead atom the proton number is ZZPbO so E_ textrmPb/mu Z^ E_mu ZPb^timesEHmu resultEPbmuP abc For positronium the only change compared to the regular hydrogen atom is that the relevant mass is only half of the electron mass. The predicted energy for the ground state is therefore E_e^+e^- fracE_ resultEposP abcliste
To test the validity of the quantum mechanical description of the hydrogen atom the energy levels of various exotic atoms have been investigated. The experimental results agree with the theoretical predictions. vspacemm Calculate the first energy level for abcliste abc a muonic hydrogen atom i.e. a hydrogen atom where the electron is replaced by a muon m_mummuO. abc a muonic lead atom. abc positronium a configuration of a positron anti-electron and an electron. Since the two masses are identical the reduced mass mum_e/ has to be used instead of the electron mass. abcliste
Solution:
The energy of the ground state of an electron in the potential of a nucleus with charge Ze is given by E_ -fracZ^ e^ m_eepsilon_^ h^ When the electron is replaced by another particle with charge -e the mass has to be adjusted accordingly. abcliste abc The energy can be calculated as E_ -fracZ^ e^ m_muepsilon_^ h^ -fracZ^ e^ m_eepsilon_^ h^fracm_mum_eE_efracm_mum_e where E_eEgrO is the energy of the ground state of the regular hydrogen atom. It follows for the myonic hydrogen atom E_mu Egrtimesfracmmume resultEHmuP abc For a muonic lead atom the proton number is ZZPbO so E_ textrmPb/mu Z^ E_mu ZPb^timesEHmu resultEPbmuP abc For positronium the only change compared to the regular hydrogen atom is that the relevant mass is only half of the electron mass. The predicted energy for the ground state is therefore E_e^+e^- fracE_ resultEposP abcliste
Meta Information
Exercise:
To test the validity of the quantum mechanical description of the hydrogen atom the energy levels of various exotic atoms have been investigated. The experimental results agree with the theoretical predictions. vspacemm Calculate the first energy level for abcliste abc a muonic hydrogen atom i.e. a hydrogen atom where the electron is replaced by a muon m_mummuO. abc a muonic lead atom. abc positronium a configuration of a positron anti-electron and an electron. Since the two masses are identical the reduced mass mum_e/ has to be used instead of the electron mass. abcliste
Solution:
The energy of the ground state of an electron in the potential of a nucleus with charge Ze is given by E_ -fracZ^ e^ m_eepsilon_^ h^ When the electron is replaced by another particle with charge -e the mass has to be adjusted accordingly. abcliste abc The energy can be calculated as E_ -fracZ^ e^ m_muepsilon_^ h^ -fracZ^ e^ m_eepsilon_^ h^fracm_mum_eE_efracm_mum_e where E_eEgrO is the energy of the ground state of the regular hydrogen atom. It follows for the myonic hydrogen atom E_mu Egrtimesfracmmume resultEHmuP abc For a muonic lead atom the proton number is ZZPbO so E_ textrmPb/mu Z^ E_mu ZPb^timesEHmu resultEPbmuP abc For positronium the only change compared to the regular hydrogen atom is that the relevant mass is only half of the electron mass. The predicted energy for the ground state is therefore E_e^+e^- fracE_ resultEposP abcliste
To test the validity of the quantum mechanical description of the hydrogen atom the energy levels of various exotic atoms have been investigated. The experimental results agree with the theoretical predictions. vspacemm Calculate the first energy level for abcliste abc a muonic hydrogen atom i.e. a hydrogen atom where the electron is replaced by a muon m_mummuO. abc a muonic lead atom. abc positronium a configuration of a positron anti-electron and an electron. Since the two masses are identical the reduced mass mum_e/ has to be used instead of the electron mass. abcliste
Solution:
The energy of the ground state of an electron in the potential of a nucleus with charge Ze is given by E_ -fracZ^ e^ m_eepsilon_^ h^ When the electron is replaced by another particle with charge -e the mass has to be adjusted accordingly. abcliste abc The energy can be calculated as E_ -fracZ^ e^ m_muepsilon_^ h^ -fracZ^ e^ m_eepsilon_^ h^fracm_mum_eE_efracm_mum_e where E_eEgrO is the energy of the ground state of the regular hydrogen atom. It follows for the myonic hydrogen atom E_mu Egrtimesfracmmume resultEHmuP abc For a muonic lead atom the proton number is ZZPbO so E_ textrmPb/mu Z^ E_mu ZPb^timesEHmu resultEPbmuP abc For positronium the only change compared to the regular hydrogen atom is that the relevant mass is only half of the electron mass. The predicted energy for the ground state is therefore E_e^+e^- fracE_ resultEposP abcliste
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