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Bess [88]
4 years ago
5

Atoms are spherical in shape. Therefore, the Pt atoms in the cube cannot fill all the available space. If only 74.0 percent of t

he space inside the cube is taken up by Pt atoms, calculate the radius in picometers of a Pt atom. The mass of a single Pt atom is 3.240 × 10−22 g. [The volume of a sphere of radius r is (4/3) πr3. The volume of a cube is l3, where l is the length of a side. Avogadro's number is 6.022 × 1023.]
Physics
1 answer:
quester [9]4 years ago
5 0

Answer:

A)6.6×10^22atoms of Pt in the cube

B)1.4×10^-8m

Explanation:

(a) Calculate the number of Pt atoms in the cube.

an edge length of platinum (Pt) = 1.0 cm.

Then Volume= 1.0 cm×1.0 cm×1.0 cm=1cm^3

Then we have volume of the cube as 1cm^3

Given:

The density Pt = 21.45 g/cm3

the mass of a single Pt atom =3.240 x 10^-22 g

Then with 1atom of the platinum element, we can calculate the number of Pt atoms in the cube as

Density of pt/mass of a single Pt atom

=(21.45 /=3.240 x 10^-22)

=6.6×10^22atoms of Pt in the cube

B)Volume of cube V=4/3πr^3

V= 4/3 ×π×r^3

V= 4.19067r^3

r^3= V/4.19067

But volume is not total volume but just 74% of it, then With 74% of the space inside the cube is taken up by Pt atoms, then we need to find 74% of volume of the cube which is 1cm^3

74/100 ×1= 0.74cm^3

Then our new volume V is 0.74cm^3

r^3=0.74/4.19067×6.620 x 10^22

r^3=2.6674×10^-24

r= 3√2.6674×10^-24

r=1.4×10^-8m

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Part b) Time to stop the car = 3.8 seconds

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Part d) Factor for stopping time is 1.

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The time required to stop the car can be found using the first equation of kinematics as

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Applying values we get

0=10.56-2.78\times t\\\\\therefore t=\frac{10.56}{2.78}=3.8seconds

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Part d)

From the relation of stopping time and the initial speed we can see that the stopping distance is proportional initial speed thus if we double the initial speed the stopping time also doubles.

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