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MDKPfromIDN

So, the temperature of a wave that has a wavelength of 5 m is [tex] \boxed{\sf{5.796 \times 10^{-4} \: K}} [/tex]

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 :

[tex] \boxed{\sf{\bold{C = \lambda_{max} \times T}}} [/tex]

With the following condition :

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

Problem Solving

We know that :

  • C = Wien's constant ≈ [tex] \sf{2.898 \times 10^{-3} \: m.K} [/tex]
  • [tex] \sf{\lambda_{max}} [/tex] = wave at its longest point = 5 m

What was asked :

  • T = absolute temperature = ... K

Step by step :

[tex] \sf{C = \lambda_{max} \times T} [/tex]

[tex] \sf{2.898 \times 10^{-3} = 5 \times T} [/tex]

[tex] \sf{T = \frac{2.898 \times 10^{-3}}{5}} [/tex]

[tex] \sf{T = \frac{2.898 \times 10^{-3}}{5}} [/tex]

[tex] \sf{T = 0.5796 \times 10^{-3}} [/tex]

[tex] \boxed{\sf{T = 5.796 \times 10^{-4} \: K}} [/tex]

Conclusion :

So, the temperature of a wave that has a wavelength of 5 m is [tex] \boxed{\sf{5.796 \times 10^{-4} \: K}} [/tex]