Question

Explore: use the gizmo to explore whether the number of atoms present affects the half-life that you measure. describe your findings below: _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________ _________________________________________________________________________

Answer 1

Answer:

The number of atoms present does not affects the half-life

Explanation:

The half-life, $t_{1/2}$ of an unstable atomic nuclei is the duration in time for the quantity of the atoms having such unstable nuclear to decrease by a factor of 2 in nature. Here nature refers to the position of the unstable nuclear in the environment. It is indicative of the rate of decay of unstable atoms and the period of survival of stable atoms

The half life is given by

$N(t) = N_0 \left (\frac{1}{2} \right )^{\frac{t}{t_{1/2}}}$

Therefore,

$t_{1/2} = \frac{t\cdot ln2}{ln(\frac{N_0}{N_t} )}$

Whereby as time time increases N₀ becomes larger such that $t_{1/2}$ remain constant.