Get the answers you need at Westonci.ca, where our expert community is dedicated to providing you with accurate information. Connect with a community of experts ready to provide precise solutions to your questions quickly and accurately. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

A radioactive material disintegrates at a rate proportional to the amount currently present. If Q(t) is the amount present at time t, then dQ/dt =−rQ where r>0 is the decay rate.

Required:
If 100 mg of a mystery substance decays to 81.14 mg in 4 weeks, find the time required for the substance to decay to one-half its original amount.


Sagot :

Answer:

For the substance to decay to one-half of its original amount, it will take:

10.6 weeks.

Step-by-step explanation:

The decay rate = dQ/dt= -rQ

Where r > 0.

100 mg of a mystery substance decays to 81.14 mg in 4 weeks

This implies that it has decayed by 18.86 mg (100 - 81.14) in 4 weeks

The rate of decay per week = 4.715 mg (18.86 mg/4)

For the substance to decay to one-half of its original amount, i.e. 50 mg (100 mg/2), it will take 10.6 (4/18.86 * 50) weeks.

We can also determine the time it will take the substance to decay by working with the decay rate and the volume of decay, thus:

Decay rate = 4.715 / week

Decay volume = 50 mg (100 mg/2)

Time for 50 mg to decay = Decay volume/Decay rate

= 50 mg/4.715

= 10.6 weeks

We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Thank you for trusting Westonci.ca. Don't forget to revisit us for more accurate and insightful answers.