**Problem 3:**For all of the remaining questions, show or describe your work.3. The mass of a sample of a mystery element is measured periodically as it decays. If 0.78% of the sample remains after 100 days, what is the half-life of the element?---**Explanation for Students:**This problem asks you to determine the half-life of an unknown element based on its decay over time. The concept of half-life is critical in understanding radioactive decay, as it represents the time required for half of the substance to decay.**Calculation Steps:**1. **Initial Setup:** - Let the initial mass be \( M_0 \). - After 100 days, 0.78% of \( M_0 \) remains.2. **Decay Formula:** - Use the exponential decay formula: \[ N(t) = N_0 \left( \frac{1}{2} \right)^{t / T_{1/2}} \] where: - \( N(t) \) is the remaining amount after time \( t \), - \( N_0 \) is the initial amount, - \( T_{1/2} \) is the half-life of the substance.3. **Substitute Known Values:** - \( 0.0078 \times M_0 = M_0 \left( \frac{1}{2} \right)^{100 / T_{1/2}} \)4. **Solve for Half-Life \( T_{1/2} \):** - Simplify the equation to solve for \( T_{1/2} \).This exercise is an application of mathematical modeling using exponential functions to describe physical phenomena. It requires algebraic manipulation and understanding of logarithms to solve for the unknown half-life.

Answered: Image /qna-images/answer/bcfe5fbb-9409-406e-a378-ce72077502ff.jpg

For all of the remaining questions, show or describe your work. 3. The mass of a sample of a mystery element is measured periodically as it decays. If 0.78 % of the sample remains after 100 days, what is the half-life of the element?

For all of the remaining questions, show or describe your work. 3. The mass of a sample of a mystery element is measured periodically as it decays. If 0.78 % of the sample remains after 100 days, what is the half-life of the element?

Chemistry

10th Edition

ISBN:9781305957404

Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste

Chapter1: Chemical Foundations

Section: Chapter Questions

Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...

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