Question

The value of absorption coefficient of black body is
A. $1$
B. $0$
C. Between $0$ and $1$
D. None of these

Answer 1

Hint: In case of a problem based on thermal properties of matter, remember the fundamental properties of a black body. Also, analyze every option with the scientific approach and check which option seems to be more appropriate for the given situation. Then, present the answer with a proper explanation.

Formula used:
The formula of Absorption Coefficient $(\alpha )$ is,
\[\alpha = \dfrac{{{Q_a}}}{Q} = \dfrac{\text{Thermal Energy Absorbed}}{\text{Thermal Energy Incident}}\]

Complete step by step solution:
A perfect black body is defined as a body that can absorb all types of radiation incident on it. Also, we know that a perfectly black body is an opaque object which means that it will not transmit any radiation directly.

The Absorption Coefficient $(\alpha )$ of a body is defined as the ratio of thermal energy (or radiation) absorbed by a body to the total thermal energy incident upon it. That is,
\[\alpha = \dfrac{{{Q_a}}}{Q} = \dfrac{\text{Thermal Energy Absorbed}}{\text{Thermal Energy Incident}}\]

A perfect black body is considered to be an ideal object which has perfect absorption of all the incident radiations with zero reflection and zero transmission. Therefore, under ideal conditions, a black body is a perfect absorber, and ${Q_a} = Q$.
\[ \therefore \alpha = \dfrac{Q}{Q} = 1\]
Thus, the value of the absorption coefficient of a perfectly black body is $1$ .

Hence, the correct option is A.

Note: The notion of such a perfect energy absorber is particularly important in the study of radiation phenomena, such as in Planck's radiation equation for the spectrum energy distribution of reemitted radiation after it has been absorbed.