Massenspektroskopie
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
\(\LaTeX\)
Need help? Yes, please!
The following quantities appear in the problem:
Masse \(m\) / elektrische Ladung \(q, Q\) / Magnetische Flussdichte \(B\) / Kraft \(F\) / Geschwindigkeit \(v\) / Radius \(r\) /
The following formulas must be used to solve the exercise:
\(F = qvB \quad \) \(F = m\dfrac{v^2}{r} \quad \)
No explanation / solution video to this exercise has yet been created.
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Visit our YouTube-Channel to see solutions to other exercises.
Don't forget to subscribe to our channel, like the videos and leave comments!
Exercise:
Ein ^textNi-Ion der Ladung +e und der Masse m .^-kg durchlaufe ein Potentialgefälle Spannung von kiloV und werde anschliess in einem Magnetfeld von .tesla abgelenkt. center tikzpicturescale. draw rectangle ; foreach x in ... foreach y in ... draw fillgray xy circle mm; node at vec B; draw fillgray! drawblack .- rectangle - node rightyshift-mm Quelle; draw very thick .-. -- -.-.; draw very thick -.-. -- -.-. nodebelow U; draw very thick -- -- --; draw very thick --. -- --. -- -. -- .; draw very thick dashed .- -- .; draw very thick dashed . arc ::.cm; draw thick-latex -- node right r .; tikzpicture center enumerate item Welchen Radius hat die Flugbahn? item Wie gross ist die Differenz der Radien zwischen einem ^textNi-Ion und einem ^textNi-Ion? enumerate
Solution:
Zuerst bestimmen wir die Geschwindigkeit des Teilchen. Dafür setzen wir die kinetische Energie der elektrischen gleich d.h. E_kin fracmv^ eU E_em Rightarrow v sqrtfraceUm. enumerate item Die resultiere Kraft ist die Lorentzkraft damit erhalten wir: F_res F_L evB mfracv^r Rightarrow r sqrtfracmUeB^ approx .m. item In einem gegebenen Magnetfeld ist der Ablenkradius proportional zur Wurzel aus der Masse des Teilchen. Daher gilt für das Verhältnis der Radien fracr_r_ sqrtfracm_m_ sqrtfrac approx .. Für den Radius der Bahn des ^textNi-Ions erhält man daher r_ approx .r_ approx .m und für die Differenz der Ablenkradien der beiden Isotope a r_-r_ approx millim. enumerate
Ein ^textNi-Ion der Ladung +e und der Masse m .^-kg durchlaufe ein Potentialgefälle Spannung von kiloV und werde anschliess in einem Magnetfeld von .tesla abgelenkt. center tikzpicturescale. draw rectangle ; foreach x in ... foreach y in ... draw fillgray xy circle mm; node at vec B; draw fillgray! drawblack .- rectangle - node rightyshift-mm Quelle; draw very thick .-. -- -.-.; draw very thick -.-. -- -.-. nodebelow U; draw very thick -- -- --; draw very thick --. -- --. -- -. -- .; draw very thick dashed .- -- .; draw very thick dashed . arc ::.cm; draw thick-latex -- node right r .; tikzpicture center enumerate item Welchen Radius hat die Flugbahn? item Wie gross ist die Differenz der Radien zwischen einem ^textNi-Ion und einem ^textNi-Ion? enumerate
Solution:
Zuerst bestimmen wir die Geschwindigkeit des Teilchen. Dafür setzen wir die kinetische Energie der elektrischen gleich d.h. E_kin fracmv^ eU E_em Rightarrow v sqrtfraceUm. enumerate item Die resultiere Kraft ist die Lorentzkraft damit erhalten wir: F_res F_L evB mfracv^r Rightarrow r sqrtfracmUeB^ approx .m. item In einem gegebenen Magnetfeld ist der Ablenkradius proportional zur Wurzel aus der Masse des Teilchen. Daher gilt für das Verhältnis der Radien fracr_r_ sqrtfracm_m_ sqrtfrac approx .. Für den Radius der Bahn des ^textNi-Ions erhält man daher r_ approx .r_ approx .m und für die Differenz der Ablenkradien der beiden Isotope a r_-r_ approx millim. enumerate
Meta Information
Exercise:
Ein ^textNi-Ion der Ladung +e und der Masse m .^-kg durchlaufe ein Potentialgefälle Spannung von kiloV und werde anschliess in einem Magnetfeld von .tesla abgelenkt. center tikzpicturescale. draw rectangle ; foreach x in ... foreach y in ... draw fillgray xy circle mm; node at vec B; draw fillgray! drawblack .- rectangle - node rightyshift-mm Quelle; draw very thick .-. -- -.-.; draw very thick -.-. -- -.-. nodebelow U; draw very thick -- -- --; draw very thick --. -- --. -- -. -- .; draw very thick dashed .- -- .; draw very thick dashed . arc ::.cm; draw thick-latex -- node right r .; tikzpicture center enumerate item Welchen Radius hat die Flugbahn? item Wie gross ist die Differenz der Radien zwischen einem ^textNi-Ion und einem ^textNi-Ion? enumerate
Solution:
Zuerst bestimmen wir die Geschwindigkeit des Teilchen. Dafür setzen wir die kinetische Energie der elektrischen gleich d.h. E_kin fracmv^ eU E_em Rightarrow v sqrtfraceUm. enumerate item Die resultiere Kraft ist die Lorentzkraft damit erhalten wir: F_res F_L evB mfracv^r Rightarrow r sqrtfracmUeB^ approx .m. item In einem gegebenen Magnetfeld ist der Ablenkradius proportional zur Wurzel aus der Masse des Teilchen. Daher gilt für das Verhältnis der Radien fracr_r_ sqrtfracm_m_ sqrtfrac approx .. Für den Radius der Bahn des ^textNi-Ions erhält man daher r_ approx .r_ approx .m und für die Differenz der Ablenkradien der beiden Isotope a r_-r_ approx millim. enumerate
Ein ^textNi-Ion der Ladung +e und der Masse m .^-kg durchlaufe ein Potentialgefälle Spannung von kiloV und werde anschliess in einem Magnetfeld von .tesla abgelenkt. center tikzpicturescale. draw rectangle ; foreach x in ... foreach y in ... draw fillgray xy circle mm; node at vec B; draw fillgray! drawblack .- rectangle - node rightyshift-mm Quelle; draw very thick .-. -- -.-.; draw very thick -.-. -- -.-. nodebelow U; draw very thick -- -- --; draw very thick --. -- --. -- -. -- .; draw very thick dashed .- -- .; draw very thick dashed . arc ::.cm; draw thick-latex -- node right r .; tikzpicture center enumerate item Welchen Radius hat die Flugbahn? item Wie gross ist die Differenz der Radien zwischen einem ^textNi-Ion und einem ^textNi-Ion? enumerate
Solution:
Zuerst bestimmen wir die Geschwindigkeit des Teilchen. Dafür setzen wir die kinetische Energie der elektrischen gleich d.h. E_kin fracmv^ eU E_em Rightarrow v sqrtfraceUm. enumerate item Die resultiere Kraft ist die Lorentzkraft damit erhalten wir: F_res F_L evB mfracv^r Rightarrow r sqrtfracmUeB^ approx .m. item In einem gegebenen Magnetfeld ist der Ablenkradius proportional zur Wurzel aus der Masse des Teilchen. Daher gilt für das Verhältnis der Radien fracr_r_ sqrtfracm_m_ sqrtfrac approx .. Für den Radius der Bahn des ^textNi-Ions erhält man daher r_ approx .r_ approx .m und für die Differenz der Ablenkradien der beiden Isotope a r_-r_ approx millim. enumerate
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