Question

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 =

Answer 1

In a scale model of a hydrogen atom with a 1.00 m diameter, the nucleus should be 0.226 mm in diameter, which would be quite challenging to construct due to the small size and required precision.

Step-by-step explanation:

To build a scale model of a hydrogen atom, an aspiring physicist should calculate the diameter of the nucleus proportionally to the diameter of the atom. Given that the diameter of a real hydrogen atom is about 1.06 × 10⁻¹⁰ m and the diameter of its nucleus is approximately 2.40 × 10⁻¹⁵ m, we need to find the scale for the model atom with a diameter of 1.00 m.

First, we calculate the ratio of the diameter of the nucleus to the diameter of the atom: (2.40 × 10⁻¹⁵ m) / (1.06 × 10⁻¹⁰ m) = approximately 2.26 × 10⁻µ. Then, to find the scale diameter of the nucleus for the model, we multiply this ratio by the model atom's diameter: 2.26 × 10⁻µ × 1.00 m = 2.26 × 10⁻µ m, or 226 × 10⁻¶ m, which is 226 micrometers or 0.226 mm. Hence, in the scale model, the diameter of the nucleus should be 0.226 mm.

To answer part (b), creating the scale model with a nucleus of 0.226 mm in diameter would be extremely challenging due to its small size and the precision required to represent it accurately at such a reduced scale.

Answer 2

a) 10.0 mm

b) 8.7 x 10¹³ times

Step-by-step 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.