stainless steel ball bearing radius 6.35 mm density 7.75 g/cm3

A stainless steel ball bearing

has a radius of 6.35 mm and a density of 7.75 g/cm3.

Iron is the principal element in steel.

Carbon is a key minor element.

The ball bearing contains 0.25% carbon, by mass.

Given that the percent natural abundance of 13C is 1.108%,

how many 13C atoms are present in the ball bearing?

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6.35 mm × (1 cm / 10 mm) = 0.635 cm

구의 부피, V

V = (4/3)πr^3

( 참고 https://ywpop.tistory.com/19756 )

= (4/3) (3.14159) (0.635 cm)^3

= 1.07253 cm^3

1.07253 cm3 × (7.75 g/cm3)

= 8.31211 g

---> ball bearing의 질량

8.31211 g × (0.25/100)

= 0.0207803 g

---> ball bearing 속 C의 질량

0.0207803 g × (1 mol / 12.01 g) × (6.022×10^23 atom/mol)

= 0.0207803 × (1 / 12.01) × (6.022×10^23)

= 1.04196×10^21 atoms of C

(1.04196×10^21 atoms) × (1.108/100)

= 1.15449×10^19 atoms of 13C

답: 1.15×10^19 atoms

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