Suppose you are given a cube made of magnesium (mg) metal of edge length 2.15 cm. (a) calculate the number of mg atoms in the cube. (b) atoms are spherical in shape. therefore, the mg atoms in the cube cannot fill all the available space. if only 74 percent of the space inside the cube is taken up by mg atoms, calculate the radius in picometers of an mg atom. (the density of mg is 1.74 g/cm3, and the volume of a sphere of radius r is 4/3π r3.) enter your answers in scientific notation.
Answers
solution:
a) To calculate the volume of cube of edge 1.0cm
Volume= (edge)³
=(100cm) ³
= 1cm³
To find the mass of MG atoms
Density = mass/volume
Mass of mg = 1.74g/cm³ x 1cm³
= 1.74g
To find the number of mg atoms,
Molar mass of mg = 24.31g
24.31g mg contain 6.022 x 10²³ atoms of mg
1.74g mg contain = 6.022 x 10²³mg atoms/24.31g mg x 1.74g mg
= 0.4310 x 10²³mg atoms
= 4.31 x 10²² mg atoms
B) to find the volume occupied by mg atoms
Total volume of cube = 1 cm³
Volume occupied by mg atoms
= 74% of 1cm³
=74/100 x 1cm³= 0.74cm³
To find the volume of 1 mg atom
4.31 x 10²² mg atoms occupy 0.74 cm³
1 atom will occupy 0.74cm³
1 atom will occupy = 0.74cm³/4.31 x 10²²mg atoms x 1mg atom
volume of 1 mg atom = 0.1716 x 10⁻²²cm²
Volume of 1 mg atom = 4/3 π³ in the form of sphere.
4/3πr³ = 0.1716 x 10⁻²²cm³
R³ = 0.1716 x 10⁻²²cm³x 4/3 x 7/22
R³ = 0.04095 x 10⁻²²cm³
R = 0.1599 x 10⁻⁷cm
1 = 10⁻¹⁰cm
= 0.1599 x 10⁻⁷cm
= 1pm/1 x 10⁻¹⁰cm x 0.1599 x 10-7cm
= 1.599 x 10² pm
R= 1.6 x 10²pm
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Answer:
Perimeter A = 122.5
Step-by-step explanation:
Set up the following proportion
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If you compare the sides opposite the angle marked with a single arc, you will get the scale factor.
If these triangles are similar, and one of the sides opposite their markings will give you the scale factor
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3r + 11
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.....
B) 4.16 · 10^-2
C) 41.6 · 10^-3
D) 0.416 · 10^-1
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Answer: B)
Step-by-step explanation:
The given product :
First open parenthesis :
Write decimal values together and power of 10s together.
Using Law of exponent :
The above expression becomes.
In scientific notation, the decimal must be placed after one digit (from left).
Hence, the correct answer is B) .
Answers
Answer: Go to a website called m a t h w a y
Step-by-step explanation:
1. It's really good for all kinds of math problems
2. It lets you answers to one question in different ways to give you the best possible answer!!!
3. IT'S FREE!!!!!!!
Answers
Answer:
it is greater than ten and less than 100, the answer is 30%
Step-by-step explanation:
600*5=3000
3000/100=30%