Question

the amount of time it takes for an amount of specific isotope to Decay to half the original amount

Answer 1

It is called Half life, to find one the formula is A=Ao(0.5)^(T/H)
A=amount 
AO=Initial Amount 
T=Time
H=Half life  

Answer 2

Answer: Half life

Explanation: Half life is the amount of time taken to reduce the original concentration of the reactant to half of its value.

Rate law expression for first order kinetics is given by:

$t=\frac{2.303}{k}\log\frac{a}{a-x}$

where,

t= time taken for the decay

k = rate constant

t = time taken for decay process

a = initial amount of the reactant

a - x = amount left after decay process

for half life: $t=t_\frac{1}{2}$

a-x = $\frac{a}{2}$

$t_\frac{1}{2}=\frac{2.303}{k}\log\frac{a}{a/2}$

$t_\frac{1}{2}=\frac{0.693}{k}$