One mole of atoms consist of 6.02 × 10^23 individual atoms. If one mole of unicorn atoms were spread uniformly over the surface of a sphere the size of the Earth, approximately how many atoms would be found per square meter? The average radius of the Earth is 6.38 × 10^3 km.

If the radius of a CD-ROM is 6 cm, what is the average area taken up by each bit if the total number of bits stored is 6 billion (6 x 109) bits?

A pyramid has a square base of side x and height h. The volume V of the pyramid is given by the expression: V - x²h 3 If V is measured to 5% and h is measured to 3%, what is the percentage uncertainty of ? Remember to include the % symbol with your answer.

One mole of Gold (Au) atom has a mass of 197 g. We know that the density of gold is 19.30 g/cm3 in room temperature. Using those numbers, answer the following questions: a) What is the mass of a single gold atom in kg? b) Assume that gold atoms sit in a perfect cubic crystal structure. Estimate the distance between two gold atoms in meters.   c) If we have a gold cube of 6 cm on each side, how many atoms can we fit along the edge of each side of the cube?  d) What would be the mass, in kilograms, of the gold cube we discussed in part (c) (measuring 6 cm on each side)?

Estimate the number of molecules that make up Earth, assuming an average molecular mass of 30 g/mol. (Note there are on the order of 1024 objects per mole.)

Grains of fine California beach sand are approximately spheres with an average radius of 50.0 μm and are made of silicon dioxide, which has a density of 2.80 × 103 kg/m3. What mass of sand grains would have a total surface area (the total area of all the individual spheres) equal to the surface area of a cube 1.10 m on an edge?

The common Eastern mole, a mammal, typically has a mass of 75 g, which corresponds to about 7.5 moles of atoms. (A mole of atoms is 6.02 * 1023 atoms.) In atomic mass units (u), what is the average mass of the atoms in the common Eastern mole?

Paperweight I bought a pack of 100 rectangular index cards. Each card measured 15 by 10 cm. The pack said ：Paper Density = 200 GSM (grams per square meter). This means that a square meter of those cards weighs 200 g. A) All of the cards in the pack are place flat on a table without overlap. In square meters, what is the total area of the table covered by the cards? B) Each pack of cards is wrapped in a sheet of 50 GSM paper with an area of 800cm squared. I have a number of packs and wish to store them on a shelf that cannot hold more than 10 kg. What is the largest whole number of wrapped packs that can be stored? C) The total weight of 500 identical sheets of paper is 2.4kg. If each sheet measures 30cm by 20cm, what is its paper density in GSM? D) A business card measures 55mm by 90mm. Its paper density is 300 GSM. Fins its exact weight in grams.

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