# Problem set 3

# Amount of Radioactive Material (number of nuclei, number of moles, weigth) and the Law of Radioactive Decay

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**1:**

Calculate the rate of disintegration of the following:

- 1.0 • 10
^{13}atoms^{99m}Tc.

- 1.0 • 10
^{14}atoms^{14}C.

- 1.0 grams
^{239}Pu.

- 1.0 gram
^{235}U.

**2:**

Calculate the amount of atoms in the following nuclides:

- 10 MBq of
^{32}P

- 200 kBq of
^{131}I

**3:**

A source of ^{60}Co has a rate of disintegration equal to 1.0 • 10^{14} Bq. What is the mass of ^{60}Co in grams?

**4:**

A preparation labelled ^{3}H disintegrates with 3.0 • 10^{5} Bq.

- What is the rate of disintegration after 3 years?

- How long does it take for the rate of disintegration to reach 2.0 • 10
^{5}Bq?

**5:**

A patient is administered 4.0 • 10^{7} Bq ^{99m}Tc in connection with a nuclear medicine examination. Calculate the amount of mass of ^{99m}Tc injected in the patient. The daughter nuclide ^{99}Tc is radioactive, but has a very long half-life. Show that the total rate of disintegration in the patient is insignificant one week after the examination.

**6:**

Calculate the rate of disintegration of the following:

- 1.0 g natural Lu-metal

- 1.0 g natural Sm-metal

**7:**

Recently it was showed that natural Bi is radioactive. How much amount of Bi is required to give a disintegration rate of 10 Bq?

**8:**

In nature ^{234}U exist in equilibrium with ^{238}U as a daughter product.

- How much
^{238}U has an equivalent disintegration rate as 1g^{234}U?

- Given the amounts from a) is separated as pure
^{238}U and^{234}U, how many percent has the amount of^{238}U decreased when the amount of^{234}U is halved?