Question

The following isotope has a half-life of 5,730 years. If we have 8.7×10-4 μμg of sample, how many years will pass until only 29% of the original sample remains. The decay follows first-order kinetics.

Answer #1

Sol :- Given initial concentration of sample say [A]_{0}
= 8.7 x 10^{-4} μμg = 8.7 x 10^{-16} g

because 1 μμg = 10^{-12} g = 1 pm

Concentration after time "t" say [A]_{t} = 29 % of 8.7 x
10^{-16} g = 2.523 x 10^{-16} g

Half life period = t_{1/2} = 5730 years

For first order kinetics

t_{1/2} = 0.693 / k

and

k = 0.693 / 5730 years = 1.209 x 10^{-4}
years^{-1}

also

From Integrated rate equation for first order reaction , we have

t = 2.303/k log [A]_{0} / [A]_{t}

t = 2.303 / 1.209 x 10^{-4} years^{-1} log 8.7 x
10^{-16} g / 2.523 x 10^{-16} g

t = 19048.8 years ( log 3.448275862)

t = 19048.8 years ( 0.5376)

**t = 10240.6 years**

The radioactive isotope 32P decays by first-order kinetics and
has a half-life = 14.3 days. How many atoms of a 1.0000 ug sample
of 32P would decay in 1.0000 second? (Assume 1 decay per atom.)

The isotope 146C has a half-life of 5,730
years. If a fossil is found to contain 1/64th the amount
of carbon-14 as is typically found in a living plant or animal, how
old is the fossil?

If the half-life of an isotope is 4 years, what fraction of the
isotope remains after 4 years? (put fraction in as decimal)

The
radioactive isotope Gold-198 has a half-life of 64.80 hrs. A sample
containing this isotope has an initial activity of 40.0 μCi.
Calculate the number of nuclei that will decay in the time interval
from 10 hrs to 12 hrs.[10 marks]

The barium isotope 133Ba has a half-life of 10.5 years. A sample
begins with 1.1×1010 133Ba atoms.
A) How many are 133Ba atoms left in the sample after 4
years.

The radioactive isotope 198Au has a half-life of 64.8 hours. A
sample containing this isotope has an initial activity at (t=0) of
1.50e-12 Bq. Calculate the number of nuclei that will decay in the
time interval between t1=10 hours and t2=20 hours
Answer is 4.60e16 but I'm not sure how. Thanks and please show
work

The radioactive isotope 198Au has a half-life of 64.8 hr. A
sample containing this isotope has an initial activity (t = 0) of
1.5x 10^12 Bq. Calculate the number of nuclei that decay in the
time interval between t1 = 10 hr and t2 = 12 hr.
Please show and explain work, and do not use calculus to solve
it.

Cs-137 is used in medical treatments. It has a half-life of 30.0
years.
How many years must pass in order for a 40.0 mg sample to decay
to 20.0 mg sample? Show your work.

Carbon-14 has a half-life of 5,730 years. A fossil is found that
has 28% of the carbon-14 found in a living sample. How old is the
fossil? (Round your answer to the nearest year.)

If the half life of Carbon 14 is about 5,730 years, then a
fossil that has 1/4 the normal proportion of Carbon 14 to Carbon 12
should be how old?
20,900
2,800
17,200
1,400
11,400

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 23 minutes ago

asked 27 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago

asked 2 hours ago