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Question: Name the part of the electromagnetic spectrum to which a wave of wavelength (i) \[1A^\circ \] and (i...

Name the part of the electromagnetic spectrum to which a wave of wavelength (i) 1A∘1A^\circ and (ii) 10−2m{10^{ - 2}}m belong. Using the relation, λT=0.29cm\lambda T = 0.29cm where the temperature is in kelvin. Calculate the kelvin temperature corresponding to these two wavelengths.

Explanation

Solution

We are asked to find the corresponding temperature to the given wavelength values. We can start by the relation given in the question. Then we can apply the value of the wavelength given in the question and find the value of temperature thus finding the required solution.

Formula used: It is given in the question that the formula to be used is, λT=0.29cm\lambda T = 0.29cm
Where TT is the temperature that is to be found
λ\lambda is the wavelength

Complete step by step solution:
Let us start by writing down the given data in the question
The formula to find the temperature is given by λT=0.29cm\lambda T = 0.29cm
Now that we have written down the value or the formula to find the temperature of the waves given. We can consider it as two cases and proceed
Case (i) When the wavelength is 1A∘1A^\circ this region is the X-ray region
Since the value of temperature can be found in kelvin using the formula λT=0.29cm\lambda T = 0.29cm
We can substitute the values as λ=1A∘\lambda = 1A^\circ but the value of wavelength should be in centimetres so we can convert it and get λ=1A∘=10−8cm\lambda = 1A^\circ = {10^{ - 8}}cm
Substituting the values, we get T=0.2910−8cm=0.29×108KT = \dfrac{{0.29}}{{{{10}^{ - 8}}cm}} = 0.29 \times {10^8}K
Now we can move onto find temperature for the second case
(ii) When the wavelength is 10−2m{10^{ - 2}}m this is the microwave region
We can substitute the values as λ=10−2m\lambda = {10^{ - 2}}m this value must be converted to centimetres λ=10−2m=10cm\lambda = {10^{ - 2}}m = 10cm is gotten once we convert it
Substitute the values in the relation λT=0.29cm\lambda T = 0.29cm
We get T=0.2910cm=0.029KT = \dfrac{{0.29}}{{10cm}} = 0.029K

Note:
Electromagnetic spectrum is the spectrum or the values of frequencies or wavelengths of electromagnetic radiation and the corresponding value of the energy of their photons. This spectrum gives us an idea about the temperature and the kinetic energies of the photons.