Question

Wavelength of Visible Light The wavelength of visible light is about \(5 \times 10^{-7}\) meter. \(^{*}\) Express this wavelength as a decimal.

Short answer

0.0000005 meters.

Step-by-step solution

Understand the Scientific Notation

The given wavelength is written in scientific notation as . This means the wavelength is represented as a number multiplied by a power of 10.

Identify the Coefficient and Exponent

In the notation

Expand the Power of 10

To convert the scientific notation to a decimal, multiply the coefficient by 10 raised to the negative exponent. This means you need to move the decimal point in the coefficient 7 places to the left.

Perform the Conversion

Move the decimal point 7 places to the left: Starting with 5, moving the decimal seven places to the left yields: 0000005.

Key concepts

wavelength

The wavelength, often denoted as \( \lambda \), is the distance between successive peaks of a wave. In the context of light, it determines the color we perceive. Wavelengths are typically measured in meters (m), but since they can be very small, we often use prefixes like nanometers (nm), where 1 nm = 10^{-9} meters.
For visible light, the wavelengths range from about 400 nm (violet) to 700 nm (red). Understanding wavelength is essential in fields like optics, astronomy, and various engineering disciplines.

visible light

Visible light refers to the portion of the electromagnetic spectrum that is visible to the human eye. It ranges from about 400 to 700 nanometers in wavelength. Visible light consists of colors ranging from violet (shorter wavelengths) to red (longer wavelengths).
This is the light we interact with daily, enabling us to see the world around us. Light behaves both as a wave and a particle, a concept known as wave-particle duality. This duality explains its many properties, including transmission, reflection, and refraction.

decimal conversion

Decimal conversion involves changing a number from one form, like scientific notation, to a decimal form. Scientific notation is useful for representing very large or very small numbers concisely as a number multiplied by a power of 10.
To convert a number like \(5 \times 10^{-7}\textrm{m}\) to decimal form, we identify the coefficient (5) and the exponent (-7). This means we move the decimal point 7 places to the left. So, \(5 \times 10^{-7} = 0.0000005 \textrm{m}\).
This conversion is crucial in scientific calculations for accuracy and simplicity.

exponent

An exponent indicates how many times a number, known as the base, is multiplied by itself. In scientific notation, the exponent tells us the number of places to move the decimal point. A positive exponent moves the decimal point to the right, while a negative exponent moves it to the left.
For example, \(10^3 \) means 10 multiplied by itself 3 times, resulting in 1000. Conversely, \(10^{-3}\) means moving the decimal point three places to the left, resulting in 0.001.
Understanding exponents is fundamental in various scientific and mathematical contexts for simplifying calculations and expressing large or small quantities efficiently.