Question

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

Answer 1

Hint: 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, \[\lambda T = 0.29cm\]
Where \[T\] is the temperature that is to be found
\[\lambda \] 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 \[\lambda T = 0.29cm\]
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 \[1A^\circ \] this region is the X-ray region
Since the value of temperature can be found in kelvin using the formula \[\lambda T = 0.29cm\]
We can substitute the values as \[\lambda = 1A^\circ \] but the value of wavelength should be in centimetres so we can convert it and get \[\lambda = 1A^\circ = {10^{ - 8}}cm\]
Substituting the values, we get \[T = \dfrac{{0.29}}{{{{10}^{ - 8}}cm}} = 0.29 \times {10^8}K\]
Now we can move onto find temperature for the second case
(ii) When the wavelength is \[{10^{ - 2}}m\] this is the microwave region
We can substitute the values as \[\lambda = {10^{ - 2}}m\] this value must be converted to centimetres \[\lambda = {10^{ - 2}}m = 10cm\] is gotten once we convert it
Substitute the values in the relation \[\lambda T = 0.29cm\]
We get \[T = \dfrac{{0.29}}{{10cm}} = 0.029K\]

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.