The isotope ^(99)Tc* is commonly used in several different types of medical imag

Question

The isotope ^(99)Tc* is commonly used in several different types of medical imaging procedures. It emits a 140-keV gamma ray (comparable to the energies of diagnostic x rays) and has half-life 6.01 h.

A. What's the change in the nuclear mass after emission of the gamma ray?

B. What's the activity of 0.62micrograms of ^(99)Tc* injected into a patient?

C. How much of ^(99)Tc* remains after one week?

D. How much of ^(99)Tc* remains after 30 days?

Note: ^(99) is to indicate the 99 is superscript (an isotope)

Explanation / Answer

a)

deltaM = E/c^2 = (140e3*1.6e-19)/(3e8*3e8) = 2.49 * 10^-31 Kg

b)

mass = 98.9062547 u = 98.9062547*1.66053e-27 = 164.24e-27 Kg

N = 0.62e-9/164.24e-27 = 3.7750e15 atomes

A = N lamda = N Ln2/T = 3.7750e15 * Ln2/(6.01*3600) = 1.21 * 10^11 Bq

c)

N = N0 (0.5)^(t/T) = 0.62e-9 * (0.5)^((7*24*3600)/(6.01*3600)) = 2.39 * 10^-18 Kg

d)

N = N0 (0.5)^(t/T) = 0.62e-9 * (0.5)^((30*24*3600)/(6.01*3600)) = 5.36* 10^-46 Kg

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