the radius of a chlorine atom is 99 pm and its mass is 5.89 X 10^-23 grams what is the density

Question

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?>?????

Answer 1

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

Answer 2

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 =

Answer 3

14.3658 g/cm^3 worked