prozess Halbwertszeit?

The correct answer is 5 min. The half-life is obtained as ln(2)/k, where k is the decay constant (where k=0.0023 s ̄1).

This can be easily calculated by placing N(t)=1⁄2N0 in the disintegration equation; then the time is exactly the half-life, and you only need to dissolve:

N(t) = N0e ̄kt
1⁄2N0 = N0 e ̄kt
ln(1⁄2)=−ln(2) = ln(e ̄kt)=−kt

t = ln(2)/k