Question

The frequency $v_m$ corresponding to which energy emitted by a black body is maximum, may vary with temperature $T$ of the body as shown in the figure. Which of the curves represents correct variation?

• A. A
• B. B
• C. C
• D. D

Answer 1

The correct option is A A

From Wein's displacement law

${\lambda }_{m}T=b$ where $b=2.898\times {10}^{-3}$...(i)

The graph for wavelength v/s temperature is a rectangular hyperbola since the relation between the quantities is inversely proportional.

$c=v\lambda$...(ii)

where $c$ is speed,$v$ frequency and $\lambda$ is wavelength of light .

substituting $\lambda$ in (i) from equation (ii)

$\frac{c}{v_m}T=b$

$v_m=\frac{c}{b}T$
Hence the relation between frequency and temperature is direct represented by a straight line passing through the origin.