the radius of a chlorine atom is 99 pm and its mass is 5.89 X 10^-23 grams what is the density
When I look at this i know that 99pm= 9.9e-7 and to get volume
v=(3/4) or 1.33
(3/4)*3.14- pi *r^3
When I get to this point I do:
1.33*3.14= 4.1762*9.9e-7= 4.1e-6pm
convert 4.1e-6pm to cm is e+10= 4.1e+4
D= mass (5.89e-27g)
________________________
Volume (4.1e+4cm^3)
= 1.4e-24
what am I doing wrong?>?????
nano = 10^-9
pico = 10^-12
1pm = 10^-12 m, so
99pm = 9.9*10^-11 m or 9.9*10^-9 cm
v = 4/3 pi r^3
so, density (mass/volume) is
5.89*10^-23 / (4/3 pi * 9.9^3 * 10^-27) = 14.49 g/cm^3
Better check my math...seems kind of high
14.3658 g/cm^3 worked
You didn't indicate units on some of this which makes it difficult to follow and you changed 5.89E-23 to 5.89E-27 in your calculations.
99 pm = 9.90E-9 cm (it's always better to convert to cm first rather than later).
volume = (4/3)*pi*r^3
volume = 4.06E-24 cc
mass = 5.89E-23/4.06E-24 =
To calculate the density of the chlorine atom, we need to consider that the given radius is in picometers (pm) and the given mass is in grams. Here are the correct steps to calculate the density:
1. Convert the radius from picometers (pm) to centimeters (cm). Since 1 pm is equal to 1e-10 cm, the radius can be converted as follows:
99 pm = 99 * 1e-10 cm = 9.9e-9 cm
2. Calculate the volume of the chlorine atom using the formula for the volume of a sphere:
V = (4/3) * π * r^3
V = (4/3) * 3.14 * (9.9e-9 cm)^3
V ≈ 4.11e-23 cm^3
3. Divide the mass of the chlorine atom by the volume to find the density:
Density = mass / volume
Density = 5.89e-23 g / 4.11e-23 cm^3
Density ≈ 1.43 g/cm^3
Therefore, the density of the chlorine atom is approximately 1.43 g/cm^3. There was an error in the calculation of the volume, which affected the final result.