
zerstreuen
to disperse
To drive apart or distribute a group of people or a collection of things in different directions.
Die Polizei zerstreute die Menschenmenge mit Wasserwerfern.
The police dispersed the crowd with water cannons.
to disperse / dispel / distract
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to disperse
To drive apart or distribute a group of people or a collection of things in different directions.
Die Polizei zerstreute die Menschenmenge mit Wasserwerfern.
The police dispersed the crowd with water cannons.

to divert oneself
To distract or entertain oneself in order to drive away worries, stress, or boredom and get one's mind on other things.
Nach der anstrengenden Woche wollte er sich am Wochenende im Kino etwas zerstreuen.
After the exhausting week, he wanted to divert himself a little at the movies over the weekend.

to dispel
To dissolve and eliminate abstract things such as concerns, doubts, fears, or rumors.
Der Arzt konnte mit seinen beruhigenden Worten alle meine Befürchtungen zerstreuen.
With his reassuring words, the doctor was able to dispel all my fears.

to distract
To disturb or distract someone's attention or concentration, so that the person becomes unfocused or mentally absent.
Der Lärm von der Baustelle zerstreute seine Gedanken, sodass er sich nicht mehr auf das Buch konzentrieren konnte.
The noise from the construction site distracted his thoughts, so he could no longer concentrate on the book.

to scatter
In physics, the phenomenon in which radiation such as light or particles is deflected in different directions through interaction with a medium.
Ein Prisma zerstreut weißes Licht in seine Spektralfarben.
A prism scatters white light into its spectral colors.
'Zerstreuen' (to disperse / dispel / distract) is an inseparable verb. The prefix 'zer-' remains firmly attached to the verb stem 'streuen' (to scatter) in all conjugated forms and sentence types.
Der Wind hat die Papiere auf meinem Schreibtisch zerstreut.
The wind scattered the papers on my desk.
The prefix 'zer-' often expresses separation, dissolution, or movement in many different directions. It intensifies the base verb 'streuen' (to scatter) into a complete distribution or dissolution.
Nach dem Konzert zerstreute sich die Menge langsam.
After the concert, the crowd slowly dispersed.
In the meaning 'auseinandertreiben' (to drive apart), the verb is mostly used with objects that refer to a group. Typical phrases are 'eine Menschenmenge zerstreuen' (to disperse a crowd), 'Demonstranten zerstreuen' (to disperse demonstrators), or 'eine Versammlung zerstreuen' (to disperse an assembly).
Die Sicherheitskräfte versuchten, die Demonstranten friedlich zu zerstreuen.
The security forces tried to disperse the demonstrators peacefully.
To express that someone distracts themselves for relaxation, the verb is used reflexively: 'sich zerstreuen' (to divert oneself). The person distracting themselves is the subject of the sentence.
Am Wochenende fahre ich ans Meer, um mich ein wenig zu zerstreuen.
At the weekend, I'm going to the sea to divert myself a little.
This meaning is used almost exclusively with abstract nouns that express a negative emotion or uncertainty. Common combinations are 'Zweifel zerstreuen' (to dispel doubts), 'Bedenken zerstreuen' (to dispel concerns), or 'Sorgen zerstreuen' (to dispel worries).
Ihre Erklärung konnte meine letzten Zweifel zerstreuen.
Her explanation was able to dispel my last doubts.
In physics, 'zerstreuen' (to scatter) is a technical term. It describes how radiation, such as light, is deflected by a medium in different directions. This use is found in scientific texts.
Die Atmosphäre zerstreut das blaue Licht der Sonne stärker als das rote.
The atmosphere scatters the sun's blue light more strongly than the red.
to drive away / distribute
Both expressions can describe an activity used to fight boredom. „Sich die Zeit vertreiben“ emphasizes that an activity makes time pass more quickly, while „sich zerstreuen“ focuses more on distracting and entertaining oneself. Use „vertreiben“ for simply passing the time; „zerstreuen“ also works for deliberate distraction.

Ich zerstreute mich nach der Arbeit mit einem Spiel.
I distracted myself with a game after work.
Ich vertrieb mir nach der Arbeit mit einem Spiel die Zeit.
I passed the time with a game after work.