The decay constant of a radioactive nuclide is 4.6 x 10^-3 s^-1. What is the half-life of the nuclide?

2.5 min

2.0 min

1.4 min

3.6 min

3.1 min

2.5s

Explanation:

Given parameters:

Decay constant of the nuclide = 4.6 x 10⁻³s⁻¹

Unkown:

Half life = ?

The half life is the time take for half of the radioactive nuclei to disintegrate. It is mathematically expressed as:

Half life = 0.693/λ

Where λ is the decay constant

Since we have been given λ we plug it into the equation:

Half life = 0.693/4.6 x 10⁻³

Half life = 0.693/0.0046

Half life = 150. 65s

Now we convert to minutes because the options are in minutes:

60s = 1 minute

150.65s = 150.65/60 = 2.5s

The half life of the nuclide is 2.5s