Question

If between wavelength $\lambda$ and $\lambda +d\lambda ,E_{\lambda }$ and $a_{\lambda }$ are the emissive and absorptive powers of a body and $E_{b\lambda }$ is the emissive power of a perfectly black body, then according to Kirchhoff's law, which of the following is true?

• A. $E_{\lambda }=a_{\lambda }=E_{b\lambda }$
• B. $E_{\lambda }{E}_{b\lambda }=a_{\lambda }$
• C. $E_{\lambda }=a_{\lambda }{E}_{b\lambda }$
• D. $E_{\lambda }{a}_{\lambda }{E}_{b\lambda }=$ constant

Answer 1

The correct option is C $E_{\lambda }=a_{\lambda }{E}_{b\lambda }$

According to Kirchhoff's law, the ratio of emissive power to absorptive power is same for all bodies and is equal to the emissive power of a perfectly black body at that wavelength i.e.
For a particular wavelength,
${\left(\frac{E}{a}\right)}_{\text{body}}=E_{\text{Black body}}$
${\left(\frac{E_{\lambda }}{a_{\lambda }}\right)}_{\text{body}}=(E_{b\lambda }{)}_{\text{Black body}}\Rightarrow E_{\lambda }=a_{\lambda }{E}_{b\lambda }$