atomar
nuclear
Refers to atoms, especially the use of nuclear energy or nuclear weapons.
Die internationale Gemeinschaft verhandelt über die atomare Abrüstung.
The international community is negotiating nuclear disarmament.

atomic / nuclear
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nuclear
Refers to atoms, especially the use of nuclear energy or nuclear weapons.
Die internationale Gemeinschaft verhandelt über die atomare Abrüstung.
The international community is negotiating nuclear disarmament.

The adjective 'atomar' (atomic / nuclear) is derived from the noun 'das Atom' (the atom). The ending '-ar' is often used to form adjectives from foreign words and means 'in the manner of' or 'related to'.
Die Spaltung eines Atomkerns setzt atomare Energie frei.
The splitting of an atomic nucleus releases atomic energy.
The meaning depends heavily on the field. In the context of politics, the military, or energy, such as 'Kraftwerk' (power plant), 'Waffe' (weapon), or 'Abrüstung' (disarmament), 'atomar' means nuclear. In the context of computer science, such as 'Operation' (operation), 'Datenbank' (database), or 'Transaktion' (transaction), it means 'unteilbar' (indivisible).
Viele Länder forschen an der Nutzung atomarer Energie.
Many countries are researching the use of nuclear energy.
In the meaning 'nuklear' (nuclear), 'atomar' is frequently combined with nouns such as 'Energie' (energy), 'Waffe' (weapon), 'Bedrohung' (threat), 'Zeitalter' (age), or 'Abfall' (waste).
Die Entsorgung von atomarem Abfall ist ein ungelöstes Problem.
The disposal of nuclear waste is an unsolved problem.
The meaning 'unteilbar' (indivisible) is purely technical language from computer science. Outside this context, the word 'atomar' (atomic) is not used or understood in this way.
Um Datenkonsistenz zu garantieren, muss der Schreibvorgang atomar sein.
To guarantee data consistency, the write operation must be atomic.
conventional
'konventionell' and 'atomar' can be understood as opposites in connection with weapons or energy. In this area, 'konventionell' means: not nuclear and not connected with weapons of mass destruction. 'atomar' refers to atoms, nuclear energy, or nuclear weapons. The risk of confusion is that in everyday language 'konventionell' only means 'usual' or 'traditional'. In military texts, the meaning is more specific: conventional weapons are precisely not nuclear weapons.

Wegen der Gefahr atomarer Waffen fordert das Land neue Gespräche.
Because of the danger of nuclear weapons, the country is calling for new talks.
Die Armee setzt in dieser Übung nur konventionelle Mittel ein.
The army is using only conventional means in this exercise.