Question

Uranium-232 has a half-life of 68.8 years. After 344.0 years, how much uranium-232 will remain from a 375.0-g sample?

Answer 1

Uranium-232 will remain 11.72 g

Further explanation

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:  

$\large{\boxed{\bold{N_t=N_0(\dfrac{1}{2})^{T/t\frac{1}{2} }}}$

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

t 1/2 = half-life  = 68.8 years

T = duration of decay  = 344 years

No= initial sample = 375 g

Uranium-232 remain :

$\tt Nt=375.\dfrac{1}{2}^{344/68.8}\\\\Nt=375.\dfrac{1}{2}^5\\\\Nt=11.72~g$