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The remaining gold-198 in the sample is 12.5 grams
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.
The main particles are emitted by radioactive elements ,so that they generally decay, are alpha (α), beta (β) and gamma (γ) particles
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
The half-life can be expressed in a decay constant (λ)
[tex]\displaystyle t_ {1/2} = {\dfrac {\ln (2)} {\lambda}}[/tex]
The half-life of Gold-198 is 3 days
Initial sample amount: 100 g
duration of decay = 9 days
Then the remaining gold-198 in the sample is
[tex]\rm \large {\boxed {\bold {N_t = 100 (\dfrac {1} {2}) ^ {\frac{9}{3} }}}}\\\\N_t=\dfrac{100}{2^3}\\\\N_t=\dfrac{100}{8}\\\\N_t=\boxed{\bold{12.5~grams}}[/tex]
examples of decay and non decay
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the exponential growth
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