The wavelength of the radiation emitted by a black body is 1 mm and Wien's constant is 3 × 10-3 mK. Then the temperature of the black body will be

Question

The wavelength of the radiation emitted by a black body is 1 mm and Wien's constant is 3 × 10-3 mK. Then the temperature of the black body will be (A) 3 K (B) 30 K (C) 300 K (D) 3000 K

Tardigrade Admin · Accepted Answer

As we know temperature of a black body is given by,

λ T = b

(Wien's displacement law)
Where, wavelength of the radiation,

λ = 1 mm = 1 \times 1 0^{- 3} m

Wien's constant,

b = 3 \times 1 0^{- 3} m K

\Rightarrow T = \frac{b}{λ} = \frac{3 \times 1 0 ^{- 3}}{1 \times 1 0 ^{- 3}} = 3 K

Q. The wavelength of the radiation emitted by a black body is 1mm and Wien's constant is 3×10−3mK. Then the temperature of the black body will be

3 K

30 K

300 K

3000 K

As we know temperature of a black body is given by, λT=b (Wien's displacement law) Where, wavelength of the radiation, λ=1mm=1×10−3m Wien's constant, b=3×10−3mK ⇒T=λb​=1×10−33×10−3​=3K

Q. The wavelength of the radiation emitted by a black body is $1 mm$ and Wien's constant is $3 \times 1 0^{- 3} m K$ . Then the temperature of the black body will be

As we know temperature of a black body is given by,
$λ T = b$ (Wien's displacement law)
Where, wavelength of the radiation,
$λ = 1 mm = 1 \times 1 0^{- 3} m$
Wien's constant, $b = 3 \times 1 0^{- 3} m K$
$\Rightarrow T = \frac{b}{λ} = \frac{3 \times 1 0 ^{- 3}}{1 \times 1 0 ^{- 3}} = 3 K$