Question

The half-life of cesium-134 is 2.06 years. If you start with 24 atoms of

cesium-134 and wait 2.06 years, how many atoms of cesium-134 will you
have left?
A. 6 atoms
B. 24 atoms
C. 48 atoms
D. 12 atoms
help please

Answer 1

Number of atoms of Cesium-134 left = 12 atoms

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((1)/(2))^{t/t(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

No=24 atoms

t1/2=2.06 years

T=2.06 years = t1/2

Since the decay time is the same as the half-life time, the number of atoms of Cesium-134 will be halved from 24 to 12.

Or we can use the formula above

`\tt Nt=24* (1)/(2)^(2.06/2.06)\\\\Nt=24* (1)/(2)=12`