If at temperature T1=1000 K, the wavelength is 2.2 × 10-6 m , then at what temperature the wavelength will be 4.4 × 10-5 m ?

Question

If at temperature T1=1000 K, the wavelength is 2.2 × 10-6 m , then at what temperature the wavelength will be 4.4 × 10-5 m ? (A) 52 K (B) 47 K (C) 49 K (D) 48 K

Tardigrade Admin · Accepted Answer

Wien's law states that λ propto (1/t) (λ1/λ2)=( T 2/ T 1) ⇒ T 2=(λ1/λ2) × T 1 =(2.2 × 10-6/4.4 × 10-5) × 1000 ∴ T 2=50 K ∴ 49 K is nearest to 50 .

Q. If at temperature $T_{1} = 1000 K$ , the wavelength is $2.2 \times 1 0^{- 6} m,$ then at what temperature the wavelength will be $4.4 \times 1 0^{- 5} m ?$

$52 K$

$47 K$

$49 K$

$48 K$

Wien's law states that $λ \propto \frac{1}{t}$
$\frac{λ _{1}}{λ _{2}} = \frac{T _{2}}{T _{1}}$
$\Rightarrow T_{2} = \frac{λ _{1}}{λ _{2}} \times T_{1}$
$= \frac{2.2 \times 1 0 ^{- 6}}{4.4 \times 1 0 ^{- 5}} \times 1000$
$∴ T_{2} = 50 K$
$∴ 49 K$ is nearest to $50.$

Q. If at temperature T1​=1000K, the wavelength is 2.2×10−6m, then at what temperature the wavelength will be 4.4×10−5m?

52K

47K

49K

48K