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Isaac Physics J2.10 - Half Lives

A 'radioactive battery' for a long range space probe uses a radioisotope with a decay constant of 4.4×10^−12 s^−1 , and a molar mass of 0.236kg. Each time one nucleus decays 2.5×10 ^−12 J of electrical energy is `made' by the generator. Calculate the mass of the radioactive sample if the spacecraft requires 200J of electricity every second (i.e. this is a 200W spacecraft). Give your answer to 2 significant figures.I can't understand why I would need the decay constant? I got my answer to be 3.1*10^-11 but its wrong :frown:
Original post by 0isab
A 'radioactive battery' for a long range space probe uses a radioisotope with a decay constant of 4.4×10^−12 s^−1 , and a molar mass of 0.236kg. Each time one nucleus decays 2.5×10 ^−12 J of electrical energy is `made' by the generator. Calculate the mass of the radioactive sample if the spacecraft requires 200J of electricity every second (i.e. this is a 200W spacecraft). Give your answer to 2 significant figures.I can't understand why I would need the decay constant? I got my answer to be 3.1*10^-11 but its wrong :frown:


It would be better that you show how you obtain 3.1*10^-11 if you still need help.
Reply 2
Original post by Eimmanuel
It would be better that you show how you obtain 3.1*10^-11 if you still need help.

Thank you for your response :smile: I got a friend to explain it to me though
Since a friend helped you, do you mind explaining how you did it here, please? I'm struggling with it too! Thanks. decay constant use a mystery too.
A 'radioactive battery' for a long range space probe uses a radioisotope with a decay constant of 4.4×10^−12 s^−1 , and a molar mass of 0.236kg. Each time one nucleus decays 2.5×10 ^−12 J of electrical energy is `made' by the generator. Calculate the mass of the radioactive sample if the spacecraft requires 200J of electricity every second (i.e. this is a 200W spacecraft). Give your answer to 2 significant figures.


Original post by Yerffoeg
Since a friend helped you, do you mind explaining how you did it here, please? I'm struggling with it too! Thanks. decay constant use a mystery too.


In Hint 3, there is an equation relating activity A, decay constant λ and number of radioactive nuclei N.
A = λN

We are given in one decay, 2.5×10−12 J of energy is produced, how many decays are required to produce 200 J in 1 second?
This number is the activity A.

The number of radioactive nuclei needed can be found using the above equation.

Number of radioactive nuclei is
number of moles × Avogadro Constant
where number of moles is the ratio of mass to molar mass.

I leave you to work out the detail.

Note that this thread would be closed soon, so if you still have any problems after reading this post, start a new thread link to this thread and describe your issue NOT just tell us you cannot get the answer. 😊

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