Question

When iridium-192 is used in cancer treatment, a small cylindrical piece of 192ir, 0.6 mm in diameter and 3.5 mm long, is surgically inserted into the tumor. if the density of iridium is 22.42 g/cm3, how many iridium atoms are present in the sample?

Answer 1

To calculate the number of iridium atoms in the sample, we need to determine the volume of the cylindrical piece of iridium-192 and the mass of iridium. The volume is calculated using the formula V = πr^2h, where r is the radius and h is the height. The mass is calculated using the density and volume. Finally, we can convert the mass to moles and multiply by Avogadro's number to find the number of iridium atoms.

Step-by-step explanation:

To calculate the number of iridium atoms present in the sample, we need to first determine the volume of the cylindrical piece of iridium-192. The volume of a cylinder is given by the formula V = πr^2h, where r is the radius of the cylinder and h is its height. In this case, the radius is half of the diameter, so r = 0.6 mm / 2 = 0.3 mm = 0.03 cm. The height is given as 3.5 mm = 0.35 cm. Plugging these values into the formula, we have V = π(0.03 cm)^2(0.35 cm) = 0.00942 cm^3.

Next, we can calculate the mass of the iridium in the sample using its density. Density is defined as mass divided by volume. Rearranging the formula, mass = density x volume. In this case, the density is given as 22.42 g/cm^3. Plugging in the values, we have mass = 22.42 g/cm^3 x 0.00942 cm^3 = 0.210 g.

Now, to determine the number of iridium atoms, we can use Avogadro's number, which tells us the number of atoms in one mole of a substance. Avogadro's number is approximately 6.022 x 10^23 atoms/mol. We need to convert the mass of the iridium sample to moles by dividing it by the molar mass of iridium. The molar mass of iridium is 192 g/mol (this can be obtained from the periodic table).

moles = mass / molar mass = 0.210 g / 192 g/mol = 0.001094 mol.

Finally, we can calculate the number of iridium atoms by multiplying the number of moles by Avogadro's number:

number of atoms = moles x Avogadro's number = 0.001094 mol x (6.022 x 10^23 atoms/mol) = 6.589 x 10^20 atoms.

Answer 2

Iridium-192 is used in cancer treatment, a small cylindrical piece of 192 Ir, 0.6 mm in diameter (0.3mm radius) and 3.5 mm long, is surgically inserted into the tumor. if the density of iridium is 22.42 g/cm3, how many iridium atoms are present in the sample?

Let us start by computing for the volume of the cylinder. V = π(r^2)*h where r and h are the radius and height of the cylinder, respectively. Let's convert all given dimensions to cm first. Radius = 0.03 cm, height is 0.35cm long.

V = π * (0.03cm)^2 * 0.35 cm = 9.896*10^-4 cm^3

Now we have the volume of 192-Ir, let's use the density provided to get it's mass, and once we have the mass let's use the molar mass to get the amount of moles. After getting the amount of moles, we use Avogadro's number to convert moles into number of atoms. See the calculation below and see if all units "cancel":

9.896*10^-4 cm^3 * (22.42 g/cm3) * (1 mole / 191.963 g) * (6.022x10^23 atoms /mole)

= 6.96 x 10^19 atoms of Ir-122 are present.