Using the equation `N = N_(0)e^(-lambdat)`, obtain the relation between half-life (T) and decay constant `(lambda)` of a radioactive substance.

Explanation

To derive the relationship between half-life (T) and decay constant (λ) of a radioactive substance using the equation \( N = N_0 e^{-\lambda t} \), we will follow these steps:

### Step 1: Understand the equation
The equation \( N = N_0 e^{-\lambda t} \) describes the number of radioactive atoms (N) remaining after time (t) given an initial number of atoms (N0) and the decay constant (λ).

### Step 2: Define half-life
The half-life (T) is defined as the time required for half of the radioactive substance to decay. Therefore, at time \( t = T \), the number of atoms remaining will be half of the initial amount:
\[
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