Question

The mass of a neon atom is \(3.35 \times 10^{-23} \mathrm{~g} .\) Express the mass as an ordinary number.

Short answer

The mass of a neon atom is 0.00000000000000000000000335 g as an ordinary number.

Step-by-step solution

Understanding Scientific Notation

Scientific notation expresses numbers that are too large or too small in a compact form using powers of ten. Here, the mass of a neon atom is given as \(3.35 \times 10^{-23} \mathrm{~g}\), which means 3.35 is multiplied by 10 raised to the power of -23.

Applying the Power of Ten

When you multiply a number by \(10^{-23}\), you move the decimal point 23 places to the left. This is because the negative exponent indicates division by a large power of ten.

Moving the Decimal Point

Start with the number 3.35. To express it as an ordinary number, move the decimal point 23 places to the left. First write 3.35 with sufficient zeros to move the decimal point past the required number of spots: 0.00000000000000000000000335.

Finalizing the Ordinary Number

After moving the decimal point 23 places left, the number becomes 0.00000000000000000000000335, which is the mass of the neon atom expressed as an ordinary number.

Key concepts

Powers of Ten

The concept of powers of ten is crucial when dealing with scientific notation. In this system, numbers are expressed as the product of two factors: a decimal fraction and a power of ten. For instance, in the expression \(3.35 \times 10^{-23}\), \(10^{-23}\) is the power of ten. This tells us the scale by which 3.35 is to be multiplied or divided. A positive exponent indicates multiplication by ten, increasing the magnitude of the number, while a negative exponent indicates division by ten, decreasing the number’s size.

• Positive exponents (e.g., \(10^2 = 100\)) make the number larger.
• Negative exponents (e.g., \(10^{-2} = 0.01\)) make the number smaller.

In the case of the neon atom mass, the power of ten is negative, showing that its actual size is much smaller than it initially appears in decimal form.

Decimal Point Movement

Moving the decimal point is the physical action that corresponds to multiplying or dividing by powers of ten in scientific notation. This step is essential when converting notation into a standard number format.For a number like \(3.35 \times 10^{-23}\), the rule is simple: the exponent tells you how many places to move the decimal point. Here, \(-23\) indicates moving the decimal point 23 places to the left.To do this:

• Start with the number, in this case, 3.35.
• Count 23 spaces to the left of the decimal point.
• Fill in the spaces with zeros as placeholders.

The result will look like a very small number: 0.00000000000000000000000335. This action effectively demonstrates the impact of dividing by an extremely large power of ten.

Neon Atom Mass

The mass of a neon atom, a very small physical quantity, demonstrates the usefulness of scientific notation and the concept of powers of ten. The mass is given as \(3.35 \times 10^{-23} \mathrm{~g}\). Without using scientific notation, such small numbers would be cumbersome and difficult to express clearly.Scientific notation allows us to simplify these expressions considerably, making it easier to grasp and communicate even minute quantities like atomic mass.

• Neon is a noble gas with very small atomic mass compared to larger units.
• Expressing its mass in scientific notation provides clarity and precision.
• This notation helps in scientific calculations, ensuring accuracy without unnecessary complexity.

By converting the scientific notation back into a standard format, we see how it represents an extremely small mass — important for understanding the scale of individual atomic particles and their properties in chemistry.