Question

The half-life of a newly discovered radioactive isotope is 6.4 hours. Initially, there are 56 grams of a sample of the isotope.

A) How many grams of the isotope remains after 24 hours? Show all of your work. Round your answer to the nearest hundredth of a gram.


B) How many hours will have passed when the sample of the isotope to reaches 6 grams? Show all of your work.

Answer 1

A) Using the attached formula where "lambda" is natural log of 2 divided by half-life. lambda = 0.69314718056 / 6.4 hours

lambda = 0.108304247 Then we use the formula:

Present Amount = Beginning Amount * e ^ (-lambda * time)

Present Amount = 56grams * 2.718281828459 ^ (-.108304247 * 24)

Present Amount = 56 * 0.0743254446

Present Amount = 4.1622248988

=4.16 grams (rounded)

B) Using the SECOND attached formula:

time = natural log (Present Amount / Bgng Amt) / -lambda

time = natural log (6 / 56) / -.108304247

time = -2.2335922219 / -.108304247

time = 20.623311493

time = 20.62 Hours

Explanation: