Question

What is the temperature of a wave that has a wavelength of 5 m?

Answer 1

So, the temperature of a wave that has a wavelength of 5 m is
`\boxed{\sf{5.796 * 10^(-4) \: K}}`

Introduction

Hi ! Here, I will help you to explain about The relationship between temperature and electromagnetic wavelength uses the principle of Wien's Constant. According to Wien, if we multiply temperature with the electromagnetic wavelengths will always got the same number (constant). Therefore, The relationship is expressed in this equation :

`\boxed{\sf{\bold{C = \lambda_(max) * T}}}`

With the following condition :

• C = Wien's constant ≈
  `\sf{2.898 * 10^(-3) \: m.K}`
• 
  `\sf{\lambda_(max)}` = wave at its longest point (m)
• T = absolute temperature (K)

Problem Solving

We know that :

• C = Wien's constant ≈
  `\sf{2.898 * 10^(-3) \: m.K}`
• 
  `\sf{\lambda_(max)}` = wave at its longest point = 5 m

What was asked :

• T = absolute temperature = ... K

Step by step :

`\sf{C = \lambda_(max) * T}`

`\sf{2.898 * 10^(-3) = 5 * T}`

`\sf{T = (2.898 * 10^(-3))/(5)}`

`\sf{T = (2.898 * 10^(-3))/(5)}`

`\sf{T = 0.5796 * 10^(-3)}`

`\boxed{\sf{T = 5.796 * 10^(-4) \: K}}`

Conclusion :

So, the temperature of a wave that has a wavelength of 5 m is
`\boxed{\sf{5.796 * 10^(-4) \: K}}`