What Range of Frequencies Corresponds to 400-700nm Wavelengths?

In summary, the human eye is sensitive to light of wavelengths from 400 to 700nm, which corresponds to a frequency range of approximately 7.5 x 10^14 Hz. This can be calculated using the formula f=v/lambda, where v is the speed of light and lambda is the wavelength.
  • #1
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Homework Statement



The human eye is sensitive to light of wavelengths from about 400 to 700nm. What range of frequencies does this range correspond to? Take the speed of light to be 3.00 x 10^8 m/s.

Homework Equations



f=v/lambda

The Attempt at a Solution



3.00 x 10^8 / 400,000m = 750 HZ

I didn't bother to find the frequency for 700nm because i know 750hz is wrong... the answer for frequency of 400nm is supposed to be 4.3x1014, but i have no idea why.
thanks for the help!
 
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  • #2
400nm is not 40,000m.
Nanometers are small. To remember the powers of 10 remember the rhyme:

"mili-micro-nano-pico"
Each is a factor of 1/1000 so 400nm = 400/(1000,000,000) meters or 4x10^ -7 m.

now v/lambda = 3/4 10^8/10^-7 = .75 x 10^(8+7) = .75 x 10^15 = 7.5 x 10^14.
Or 750,000,000,000,000 equals (let's see kilo-mega-giga-tera) 750TeraHz.
 

FAQ: What Range of Frequencies Corresponds to 400-700nm Wavelengths?

What is the relationship between wavelength in nm and frequency?

The relationship between wavelength in nm and frequency is inverse, meaning that as the wavelength decreases, the frequency increases and vice versa. This is described by the equation: frequency = speed of light / wavelength.

How do you convert between wavelength in nm and frequency?

To convert from wavelength in nm to frequency, divide the speed of light (3.00 x 10^8 m/s) by the wavelength in nm. The result will be in units of hertz (Hz).

What is the significance of using nanometers (nm) for measuring wavelength?

Nanometers are used to measure wavelength because they are a more precise unit of measurement for the small wavelengths of light. They are widely used in the scientific community for various applications, including measuring the electromagnetic spectrum.

Can you give an example of a wavelength in nm and its corresponding frequency?

One example of a wavelength in nm is 500 nm, which corresponds to a frequency of 6.00 x 10^14 Hz. This is the wavelength of green light, which has a frequency of 600 THz (terahertz).

Why is it important to understand the relationship between wavelength in nm and frequency?

Understanding the relationship between wavelength in nm and frequency is crucial in many scientific fields, including physics, chemistry, and astronomy. It allows scientists to accurately measure and describe the properties of light and other electromagnetic radiation, which has many practical applications in technology and research.

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