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Physics Question! Nuclear Decay HELP!?
I have an exam in a couple in a couple of weeks and came across this question in a past paper, can anybody give me a detailed solution? It would be greatly appreciated!
Technetium-99 (Tc-99) is a radioisotope tracer with a decay constant, k (it should be lambda I don't know how to insert it) of 0.12 hr^-1. It emits 140 keV gamma photons and is commonly used in nuclear medicine to study the functionality of body organs and systems. A patient undergoing a bone scan is injected with Tc-99 with activity 800 MBq. After how long will the total amount of gamma energy emitted from the patient every second fall to 1.0 μJ?
2 Answers
- Steve4PhysicsLv 77 years agoFavorite Answer
Is that really an exam question??? They are usually split into parts to guide you through and allow at least some marks to be obtained by students unable to answer the whole question.
140keV = 140 x 1000 x 1.6x10⁻¹⁹J. Work this out. I'll call this 'E'.
1μJ/s = 1x10⁻⁶ J/s is being emitted. Therefore the number of photons emitted per second is 1x10⁻⁶/E. Work this out. I'll call 'A'.
A is the simply the number of decays/second, i.e. the activity, after time t.
A = A₀e^(-λt) where A₀ = 800x10⁶ Bq and λ = 0.12 hr⁻¹
Substitute the values for A. A₀ and λ, and you can solve to find t (This requires taking natural logarithms of both sides of the equation in the usual way for solving exponentials.)
- 7 years ago
Wow, I think injecting people with radioactive isotopes is an extremely dangerous and horrific thing to do.
