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(+) | 100% | THE PROBLEM The useful lifetime of the Mössbauer Spectrometer on a

ID: 587504 • Letter: #

Question

(+) | 100% | THE PROBLEM The useful lifetime of the Mössbauer Spectrometer on a Rover depends on the lifetime of the emission of gamma rays at a particular minimum level by a 10 mg sample of cobalt-57. How long will the initial amount of cobalt be useful in the Mössbauer spectrometer? Radioactive decay is unchanged by temperature chemistry, and environmental conditions. Your goal is to determine the length of time that the Mössbauer spectrophotometer on the amount of sco remaining is 1 mg or less. The half life of so is 212 days. The time of travel from earth to Mars is seven months. Mars Rover can continue to collect data if it will no longer work when the

Explanation / Answer

Given the half-life of Co57 is 212 days.

Radio active decay follows the first order reaction.

Relation between the rate constant and half life of the reaction is:

K= 0.693/t1/2. -----------------(1)

Where K = rate constant of the reaction

t1/2= half-life of the radio active decay

Substitute the given t1/2 value in the above equation to get K value.

K= 0.693/212 days

Use this K value to find the required time period.

K= (2.303/t) . log a/a-x ---------------(2)

Where a= initial concentration of the substrate

a-x = amount left after time period t

Substitute the above given values in (2)

0.693/212days = 2.303/t. log(10mg/1mg)

=> t =2.303x212days/0.693. [Since log10=1]

t=704.5 days

Hence,the time taken is 704.5 days