The diameter of a hydrogen atom is approximately 1.06 ✕ 10−10 m, as defined by the diameter of the spherical electron cloud around the nucleus. the hydrogen nucleus has a diameter of approximately 2.40 ✕ 10−15 m. (a) imagine a scale model of a hydrogen atom where its diameter is represented by the height of the empire state building (1454 ft to the top of its antenna). in this model, what would be the diameter of the nucleus in millimeters? mm (b) the atom is how many times larger in volume than its nucleus? va vn =

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.        

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