The heaviest member of the alkaline earth metals is radium...

The heaviest member of the alkaline earth metals is radium (Ra), a naturally radioactive element discovered by Pierre and Marie Curie in $1898 .$ Radium was initially isolated from the uranium ore pitchblende, in which it is present as approximately 1.0 g per 7.0 metric tons of pitchblende. How many atoms of radium can be isolated from $1.75 \times 10^{8} \mathrm{g}$ pitch-blende $(1 \text { metric ton }=1000 \mathrm{kg})$ ? One of the early uses of radium was as an additive to paint so that watch dials coated with this paint would glow in the dark. The longest-lived isotope of radium has a half-life of $1.60 \times 10^{3}$ years. If an antique watch, manufactured in $1925,$ contains 15.0 $\mathrm{mg}$ radium, how many atoms of radium will remain in 2025$?$

Key Concepts

Half-life

The half-life of a radioactive substance is the time required for half of the original amount of the substance to decay. It is a critical concept in nuclear chemistry and physics, as it quantifies the rate of decay and allows calculation of the remaining amount of a radioactive material after a given period using exponential decay formulas.

Avogadro's Number

Avogadro's Number, approximately 6.022 × 10^23, is the number of atoms or molecules in one mole of a substance. This fundamental constant is essential for converting a mass of a substance into the corresponding number of atomic or molecular units, making it a cornerstone in calculations that link microscopic particles to macroscopic measurements.

Radioactive Decay

Radioactive decay is the spontaneous process by which an unstable atomic nucleus loses energy by emitting radiation. This concept is key in understanding how the quantity of a radioactive isotope decreases over time, and it is characterized by an exponential decay behavior that depends on the half-life of the element.

Stoichiometry

Stoichiometry involves using mass, molar masses, and ratios to calculate the quantities of reactants and products in chemical processes. It allows scientists to relate the mass of materials, such as ores containing trace amounts of an element, to the number of atoms or moles present, thus bridging macroscopic measurements with atomic-scale entities.

Unit Conversion

Unit conversion is the process of converting one measurement unit into another, ensuring that calculations are performed with consistent dimensions. In chemistry, converting between units such as grams, kilograms, and metric tons is crucial for determining the correct amount of a substance when relating mass to other properties like moles or atoms.

Transcript

00:01 So in this video, we're going to work through question 116 from chapter 20, which says the heaviest number of the alkaline earth metals is radium, a naturally radioactive element discovered by pierre and marie curie in 1898.

00:14 Radium was initially isolated from the uranium or pitch blend in which it is present as approximately 1 gram per 7 metric tons of pitch blend.

00:23 How many atoms of radium can be isolated from 1 .75 times 10 to the 8th grams of pitch blend, given that we're, one metric ton is equal to 1 ,000 kilograms.

00:36 One of the early uses of radium was as an additive to paint so that watch dials coded that this paint could glow in the dark.

00:44 The longest -lived isotope of radium has a half -life of 1 .6 times 10 to the third years.

00:50 If an antique watch manufactured in 1925 contains 15 milligrams of radium, how many atoms of radium will remain in 2025? so let's start out with this first question, how many atoms of radium can be isolated from 1 .75 times 10 to the 8th grams of pitch blend? so we start out with our 1 .75 times 10 to the 8th grams of pitch blend, or i've written that here as pb, and then i know that there are 1 ,000 grams in 1 kilogram and 1 ,000 kilograms in one tonne.

01:26 So i'm converting this to tons of pitch blend.

01:29 And then i know that for every, every seven times of pitch blend, i have one gram of radium.

01:35 So now i'm in grams of radium at this point in the calculation.

01:40 Then i can use my molar mass to convert grams to moles of radium.

01:44 So i divide by the molar mass.

01:46 And then i know that i have an avogadro's number of atoms in one mole.

01:51 So i have 6 .02 times 10 to the 23rd atoms of radium per one mole of radium.

01:57 So all of this evaluates to 6 .78 times 10 to the 22nd atoms of radium...

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