The maximum energy in the thermal radiation from a hot source occurs at a wavelength of 11 × 10-5 cm. According to Wien's law, the temperature of the source(on Kelvin scale) will be n times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is 5.5 × 10-5 cm. The value of n is

Question

The maximum energy in the thermal radiation from a hot source occurs at a wavelength of 11 × 10-5 cm. According to Wien's law, the temperature of the source(on Kelvin scale) will be n times the temperature of another source (on Kelvin scale) for which the wavelength at maximum energy is 5.5 × 10-5 cm. The value of n is (A) 2 (B) 4 (C) 1/2 (D) 1

Tardigrade Admin · Accepted Answer

According to Wien's law, λm T= constant ∴ (λm)1 T1=(λm)2 T2 or (11 × 10-5) T1=(5.5 × 10-5) T2 or T1=(1/2) T2 ∴ n=(1/2)

2

4

1/2

1

According to Wien's law, λm​T= constant ∴(λm​)1​T1​=(λm​)2​T2​ or (11×10−5)T1​=(5.5×10−5)T2​ or T1​=21​T2​ ∴n=21​

According to Wien's law, $λ_{m} T =$ constant
$∴ (λ_{m})_{1} T_{1} = (λ_{m})_{2} T_{2}$
or $(11 \times 1 0^{- 5}) T_{1} = (5.5 \times 1 0^{- 5}) T_{2}$ or
$T_{1} = \frac{1}{2} T_{2}$
$∴ n = \frac{1}{2}$