Match the temperature of a black body given in List- I with an...

Maximum wavelength for each case:

$\left(P\right)2000K$	${\lambda}_{m}T = b$ $⇒ {\lambda}_{m} = \dfrac{b}{T} = \dfrac{2 . 9 \times {10}^{- 3}}{2000} = 1 . 45 \times {10}^{- 6}m = 1450nm$
$( Q ) 3000K$	${\lambda}_{m}T = b ⇒ {\lambda}_{m} = \dfrac{2 . 9 \times {10}^{- 3}}{3000} = 966 . 66nm$
$( R ) 5000K$	${\lambda}_{m}T = b ⇒ {\lambda}_{m} = \dfrac{2 . 9 \times {10}^{- 3}}{5000} = 580nm$
$( S ) 10000K$	${\lambda}_{m}T = b ⇒ {\lambda}_{m} = \dfrac{2 . 9 \times {10}^{- 3}}{10, 000} = 290nm$

Now for List-$II$:

\left(1\right){\lambda}_{th} = \dfrac{hc}{ϕ} = \dfrac{1 . 24 \times {10}^{- 6}}{4} = 0 . 31 \times {10}^{- 6}m = 310nm$</p><p>For$\lambda \le {\lambda}_{th}$, emission of photoelectrons will take place. Therefore,$S \to 1$.</p><p>$\left(2\right)$Wavelength range visible to human eye ranges from$400\text{to}700nm$. Therefore,$R \to 2$.</p><p>$\left(3\right)$Width of the central maxima is directly proportional to the wavelength of the light used. Therefore, for maximum width, maximum wavelength is required. Hence,$P \to 3$.</p><p>$\left(4\right)$Power emitted by blackbody is given by, </p><p>$\sigma{\left({T}_{1}\right)}^{4} = \dfrac{1}{16}\left(\sigma{T}^{4}2\right) ⇒ {T}_{1} = \dfrac{1}{2}{T}_{2} = 3000K$</p><p>Therefore,$Q \to 4$.</p><p>\left(5\right)$ For imaging bones $X$-rays are used in the wavelength range of $1 - 10nm$. None of the options in List-$I$ matches with it.