G
Guest
Guest
1. The rate of decay of a radioactive element is such that, when the mass present is M, DM/dt = -km, where k is a constant.
a. Verify that the mass function M = M<sub>0</sub>e<sup>-kt</sup>, where M<sub>0</sub> is a constant, satisfies this condition.
b. If the “half-Life” period of the element (i.e. the time required for M<sub>0</sub> to reduce to (1/2)Mo<sub>0</sub>) is T, prove that k = ln(2) / T.
2. A substance contains two radio-active elements A and B with “Half-Life” periods T<sub>1</sub> and T<sub>2</sub>, respectively, and T<sub>1</sub> > T<sub>2</sub>. Initially, the mass of B is twice that of A. Find when the substance will contain equal masses of A and B.
Thank you in advance
a. Verify that the mass function M = M<sub>0</sub>e<sup>-kt</sup>, where M<sub>0</sub> is a constant, satisfies this condition.
b. If the “half-Life” period of the element (i.e. the time required for M<sub>0</sub> to reduce to (1/2)Mo<sub>0</sub>) is T, prove that k = ln(2) / T.
2. A substance contains two radio-active elements A and B with “Half-Life” periods T<sub>1</sub> and T<sub>2</sub>, respectively, and T<sub>1</sub> > T<sub>2</sub>. Initially, the mass of B is twice that of A. Find when the substance will contain equal masses of A and B.
Thank you in advance