Question

Certain substance emits only the wavelengths, ${\lambda _1}$, ${\lambda _2}$, ${\lambda _3}$, and ${\lambda _4}$ when it is at a high temperature. When this substance is at a colder temperature, it will absorb only the following wavelengths:
(A) ${\lambda _1}$
(B) ${\lambda _2}$
(C) ${\lambda _1}$ and ${\lambda _2}$
(D) ${\lambda _1}$, ${\lambda _2}$, ${\lambda _3}$, and ${\lambda _4}$

Answer 1

This question uses the concept of spectroscopy and its laws. You need to know about Kirchhoff's Law of spectroscopy, in order to solve this question. Moreover, you can get an answer by looking at the expression for Kirchhoff’s law, which states that the emissivity is equal to absorptivity.

Complete step by step answer:
As we all know that the expression for the Kirchhoff’s Law of spectroscopy is given as,
$\varepsilon = \alpha$
Here, $\varepsilon$ is the emissivity and $\alpha$ is the absorptivity.
According to the expression, it can be understood that if a substance or a body emits a particular wavelength at a very high temperature. Then at a comparatively lower temperature, that substance or body will only absorb the same or equivalent wavelength. The substance will not absorb any other wavelength at a lower temperature. So according to the law, the total emissivity of the body is equal to total absorptivity.
A body under certain different conditions produces a different spectrum of light and wavelength. For example, a hot solid produces a continuous spectrum under high pressure.
So in our question, substance emits only the wavelength, ${\lambda _1}$, ${\lambda _2}$, ${\lambda _3}$, and ${\lambda _4}$ at higher temperature. This means that substance will only absorb same emitted wavelength, ${\lambda _1}$, ${\lambda _2}$, ${\lambda _3}$, and ${\lambda _4}$ at a colder temperature. It means that the substance emitting wavelength ${\lambda _1}$ at higher temperature, will absorb the same wavelength ${\lambda _1}$ at lower temperature. Similarly, the substance emitting wavelength ${\lambda _2}$ at higher temperature, will absorb the same wavelength ${\lambda _2}$ at lower temperature.
So, the substance will absorb wavelength ${\lambda _1}$, ${\lambda _2}$, ${\lambda _3}$, and ${\lambda _4}$ at a colder temperature.

So, the correct answer is “Option D”.

Note:
You need to be clear that the substance emitting wavelength at a higher temperature will absorb the same wavelength at a lower temperature.
You can make mistakes if you do not know about Kirchhoff’s Law.