(a) Explanation Given information: A 100-mg of cesium-137 is provided and its half-life is 30 years. Formula used: The mass of radioactive substance decays exponentially in the form of the equation m ( t ) = m 0 e k t , where m ( t ) is the mass remaining of a substance from an initial mass m 0 after time t . Calculation: A 100-mg of cesium-137 is provided with half-life is 30 years. Since the mass of radioactive substance decays exponentially in the form of the equation m ( t ) = m 0 e k t , where m ( t ) is the mass remaining of a substance from an initial mass m 0 after time t . Therefore, mass remaining after 30 years is 50-mg. Substitute m ( t ) as 50, t as 30 and m 0 as 100, in the equation m ( t ) = m 0 e k t to solve for k . 50 = 100 e 30 k 1 2 = e 30 k Take natural log in both the sides of the equation, ln 1 2 = ln e 30 k Recall that ln x a = a ln x and ln e = 1 , apply it, ln 1 2 = 30 k ln e ln 1 2 = 30 k 1 30 ln 1 2 = k ln (b) To determine To calculate: The mass of cesium-137 that remains after 100 years. (c) To determine To calculate: The rate of decay for cesium-137 after 100 years. (d) To determine To calculate: The number of years till which only 1 gm of sample remains.

15th Edition

ISBN: 9781133109631

Author: Stewart, JAMES, Day, Troy

Publisher: Cengage Learning,

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Chapter 3.6, Problem 7E

(a)

To determine

To calculate: The mass of cesium-137 that remains after t years.

(b)

To determine

To calculate: The mass of cesium-137 that remains after 100 years.

(c)

To determine

To calculate: The rate of decay for cesium-137 after 100 years.

(d)

To determine

To calculate: The number of years till which only 1 gm of sample remains.

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The mass of cesium-137 that remains after t years.

Solution Summary: The author calculates the mass of cesium-137 that remains after t years using the equation m(t)=m_0ekt.

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To calculate: The mass of cesium-137 that remains after t years.

To calculate: The mass of cesium-137 that remains after 100 years.

To calculate: The rate of decay for cesium-137 after 100 years.

To calculate: The number of years till which only 1 gm of sample remains.

Chapter 3 Solutions