Question

What is the time that takes for half of the atoms of a radioactive element to decay?

Answer 1

Radioactive Decay – Measuring the Age of the Solar System The half-life of a radioactive element is the amount of time it takes for half of the atoms in a sample to decay from an unstable state to a stable one.

Answer 2

Explanation:

Answer: It will take 22920 years to decay 112.5 g of 120 grams.

Explanation: Radioactive decay follows first order kinetics.

Half-life of carbon-14 = 5730 years

\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{5730}=1.209\times 10^{-4}year^{-1}λ=

t

2

1

0.693

=

5730

0.693

=1.209×10

−4

year

−1

N=N_o\times e^{-\lambda t}N=N

o

×e

−λt

N = amount left after time t = (120-112.5)g= 7.5 g

N_0N

0

= initial amount = 120 g

\lambdaλ = rate constant =1.209\times 10^{-4}year^{-1}1.209×10

−4

year

−1

t= time = ?

7.5=120\times e^{- 1.209\times 10^{-4}years^{-1}\times t}7.5=120×e

−1.209×10

−4

years

−1

×t

t=22920yearst=22920years