Use the following equations to calculate the ratio of parent -to- daughter isoto

Question

Use the following equations to calculate the ratio of parent -to- daughter isotopes after 1 billion years for the parent-daughter isotope system 238^U to^206 Pb (2 credits). N_D = N_p(e^lambdat1/2 -w1) t^1/2 = 0.697/lambda where N_D is the numbers of daughter isotopes produced by radioactive decay, N_p is the number of parent isotopes remaining, A is the decay constant for the parent-daughter isotope system and t_1/2 is the half-life for the parent-daughter isotope system. You should use the half-life which is given in chapter 12 of Earth: Portrait of a Planet by S. Marshak. Highlight and replace the question mark (?) with your answer. Round off your answer to 2 decimal places. Parent- to- daughter ratio = 1 to |

Explanation / Answer

half-life t1/2 for the decay = 4.47 billion years

so,

decay constant l = 0.693/4.47 = 0.155 billion years -1

ratio of daughter/parent nuceli = N(D)/N(p) = e^(l.t) - 1)

t = 1 billion years

feed the values,

N(D)/N(p) = e^(0.155 x 1) - 1

                 = 0.17

Parent-to-daughter ratio = 1 to 0.17

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