Answer:
a) 10.0 mm
b) 8.7 x 10¹³ times
Explanation:
Atom diameter = 1.06 x 10⁻¹⁰ m ________________ 100%
Nucleus diameter = 2.40 x 10⁻¹⁵ m ______________ x
x = 2.26 x 10⁻³ %
The nucleus diameter is equivalent to 2.26 x 10⁻³ % of the total atom size.
a) The Empire State Building model:
1 ft = 304.8 mm
1454 ft = 443179.2 mm
443179.2 mm______ 100%
y ______ 2.26 x 10⁻³ %
y = 10.0 mm
In this model, the diameter of the nucleus would be 10.0 mm.
b) Sphere volume: V =(4 · π · r³
)/3
V atom = (4 . π .( 0.53x10⁻¹⁰)³ )/3
V atom = 6.2 x 10⁻³¹ m³
V nucleus = (4 . π .( 1.2x10⁻¹⁵)³ )/3
V nucleus = 7.2 x 10⁻⁴⁵ m³
V atom / V nucleus = 6.2 x 10⁻³¹ m³ / 7.2 x 10⁻⁴⁵ m³
V atom / V nucleus = 8.7 x 10¹³
The atom is times 8.7 x 10¹³ larger in volume than its nucleus.
