Question

A nuclide has a half life of 2.41 x104 years. How long will it take a...

A nuclide has a half life of 2.41 x104 years. How long will it take a sample to reach a level of radioactivity that is 2.5% the level it had when it was first made?

Homework Answers

Answer #1

Radio active decay is a first order reaction.

For first order recation,

half life t1/2 = 0.693 /k where k is rate constant

k = 0.693/ t1/2 --- Eq (1)

k = 1/t ln { [A]o/[A]t} -----Eq (2)

From Eqs (1) and (2),

0.693/ t1/2 = (1/t) ln {[A]o/ [A]t} ------Eq (3)

Given that

half life t1/2= 2.41 x104 yrs = 24100 yrs

time t = ? hrs

Initial radioactivity  [A]o = 100 %

Final radioactivity   [A]t = 2.5 %

Substitute all the values in Eq (3),

0.693/ t1/2 = (1/t) ln {[A]o/ [A]t}

[(0.693)/ 24100 yrs)] = (1/t )  ln{100/2.5}

t = ln {100/2.5} x ( 24100 yrs/ 0.693)

= 128285 yrs

t = 128285 yrs

Therefore, 128285 yrs required to reach a level of radioactivity that is 2.5% the level it had when it was first made.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
The nuclide As-76 has a half-life of 26.0 hours. If a sample of As-76 weighs 344...
The nuclide As-76 has a half-life of 26.0 hours. If a sample of As-76 weighs 344 g, what mass of As-76 remains after 6.00 days? Hint: calculate k first.
The half-life of oxygen-50 is about 5 730 years. How long does it take a 100...
The half-life of oxygen-50 is about 5 730 years. How long does it take a 100 g sample to decay to 12.5 g?
A radioactive nuclide has a half-life of 30.7 y. What fraction of an initially pure sample...
A radioactive nuclide has a half-life of 30.7 y. What fraction of an initially pure sample of this nuclide will remain undecayed at the end of 86.8 y?
You have a sample of a radioactive material with a half-life of 5.0 years that has...
You have a sample of a radioactive material with a half-life of 5.0 years that has a current activity of 0.12 µCi. The sample has a label on it which indicates that when it was first manufactured it had an activity of 3.84 µCi. How long ago was the sample manufactured? (to 2 s.f and in years)
The radioactive nuclide Plutonium-199 has a half-life of 43.0 min. A sample is prepared that has...
The radioactive nuclide Plutonium-199 has a half-life of 43.0 min. A sample is prepared that has an initial activity of 7.56 ×1011 Bq. i. How many Plutonium-199 nuclei are initially present in the sample? ii. How many are present after 30.8 min? iii. What is the activity at this time?
15.58 The half-life for the radioactive decay of C−14 is 5730 years. How long will it...
15.58 The half-life for the radioactive decay of C−14 is 5730 years. How long will it take for 25% of the C−14 atoms in a sample of C−14 to decay? If a sample of C−14 initially contains 1.9 mmol of C−14, how many millimoles will be left after 2250 years?
The half-life for the radioactive decay of C−14 is 5730 years. Part A: How long will...
The half-life for the radioactive decay of C−14 is 5730 years. Part A: How long will it take for 25% of the C−14 atoms in a sample of C−14 to decay? Part B: If a sample of C−14 initially contains 1.9 mmol of C−14, how many millimoles will be left after 2255 years?
The half-life of Sr 90 is 28 years A. how many grams of Sr 90 in...
The half-life of Sr 90 is 28 years A. how many grams of Sr 90 in a 8.00 g sample of this nuclide will have decayed after 84 years? B. how many hours are required to reduce the amount of Sr 90 present in 80.0g sample to 10.0mg?
188Re has a half-life of 17.0 hr. How long will it take for 5 mg of...
188Re has a half-life of 17.0 hr. How long will it take for 5 mg of the isotope to decay to 0.5 mg? a. 56 hr b. 27 hr c. 9.4 hr d. 0.094 hr e. 5.6 hr
the half life of radioactive iodine is 8 days, how long will it take for 10g...
the half life of radioactive iodine is 8 days, how long will it take for 10g of radioactive iodine to decrease to 1.25g?