B. 11,540
The atomic nucleus can experience decay into 2 particles or more due to the instability of its atomic nucleus.
Usually radioactive elements have an unstable atomic nucleus.
General formulas used in decay:
[tex]\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{t/t\frac{1}{2} }}}[/tex]
T = duration of decay
t 1/2 = half-life
N₀ = the number of initial radioactive atoms
Nt = the number of radioactive atoms left after decaying during T time
Nt=25 g
No=100 g
t1/2=5770 years
[tex]\tt 25=100\dfrac{1}{2}^{T/5770}\\\\\dfrac{1}{4}=\dfrac{1}{2}^{T/5770}\\\\2=T/5770\rightarrowT=11540~years[/tex]
