A hydrogen atom has a diameter of about 10 nm. Express this diameter in micrometers, meters, and millimeters.

1) 1 nm = 0.001 µm; which indicates that one nanometer equals 0.001 (10⁻³) micrometer.

d(H) = 10 nm; the diameter of a hydrogen atom.

d(H) = 10 nm · 0.001 µm/nm.

d(H) = 0.01 µm = 10⁻² µm.

2) 1 nm = 10⁻⁹ m; illustrating that one meter is equivalent to 0.000000001 (10⁻⁹) meter.

d(H) = 10 nm.

d(H) = 10 nm · 10⁻⁹ m/nm.

d(H) = 0.00000001 m = 10⁻⁸ m.

3) 1 nm = 10⁻⁶ mm; showing that a nanometer corresponds to 0.000001 (10⁻⁶) millimeter.

d(H) = 10 nm · 10⁻⁶ mm/nm.

d(H) = 0.00001 mm = 10⁻⁵ mm.

The diameter of a hydrogen atom, which is 10 nm, can be represented in micrometers, meters, and millimeters as follows: 10⁻² μm, 10⁻⁸ m, and 10⁻⁵ mm

Additional Clarification

Magnitude refers to what can be measured or quantified.

The principal amount signifies the value established through scientific consensus.

Derived magnitude is a quantity obtained from the principal amount.

There are seven primary quantities defined by international standards, specifically:

• 1. Length, measured in meters (m)
• 2. Time, measured in seconds (s)
• 3. Mass, measured in kilograms (kg)
• 4. Temperature, measured in kelvin (K)
• 5. Light intensity, measured in candela (cd)
• 6. Electric current, measured in ampere (A)
• 7. Amount of substance, measured in moles (mol)

The concept of length is intended to illustrate distance between two points

It is typically denoted by the symbol l, length

Length can be measured using tools such as rulers, calipers, meters, or screw micrometers

Primary length units consist of seven units, in addition to various length units such as inches, miles, yards, and feet:

• Kilometer, km
• Hectometer, hm
• Dekameter, dam
• Meter, m
• Decimeter, dm
• Centimeter, cm
• Millimeters, mm

Each unit is scaled down by multiplying by 10, and increasing one unit is achieved by dividing by 10.

Conversions for other mass units:

mm (millimeters) = 10⁻³ m

km (kilometers) = 10³ m

µm (micrometers) = 10⁻⁶ m

nm (nanometers) = 10⁻⁹ m

Gm (gigameters) = 10⁹ m

ρm (picometers) = 10⁻¹² m

A hydrogen atom's diameter is about 10 nm.

Thus, in micrometers: µm = 10⁻⁹ / 10⁻⁶ · 10 = 10⁻²

In meters: 10⁻⁹ m · 10 = 10⁻⁸

And in millimeters: 10⁻⁹ / 10⁻³ · 10 = 10⁻⁵

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