Question

The isotope 198 au (atomic mass = 197.968 u) of gold has 79 a half-life of 2.69 days and is used in cancer therapy. what mass (in grams) of this isotope is required to produce an activity of 315 ci?

Answer 1

391.12 * $10^{16}$ mass is required for activity of 315 ci

The activity of the radioactive substance is the number of disintegrations taking place in a radioactive sample.

Isotopes are the members of an element having the same number of protons but the different number of neutrons.

the activity of the radioactive sample is given as:

A = λ * N

where λ is the decay constant and N is the number of disintegrations.

activity is given as 315 ci

A = 315 * 3.7 * $10^{10}$

   = 1165.5 *  $10^{10}$ Bq

λ = 0.693 / $t_{1/2}$

   = 0.693 / 2.69 * 24 * 3600

   = 2.98 * $10^{-6}$ t^-1

Therefore, N = A /  λ

                      = 1165.5 *  $10^{10}$ /  2.98 * $10^{-6}$

                  N = 391.12 * $10^{16}$

391.12 * $10^{16}$ mass is required for activity of 315 ci

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