Question

Three black discs 'x', 'y', 'z' have radii 1m, 2m, and 3m respectively. The wavelengths corresponding to maximum intensity are 200, 300, and 400 nm respectively. The relation between emissive powers 'E_x', 'E_y' and 'E_z' is ______.

Options

• E_x > E_y > E_z

• E_x < E_y < E_z

• E_x = E_y = E_z

• E_x > E_y > E_z

Answer 1

Three black discs 'x', 'y', 'z' have radii 1m, 2m, and 3m respectively. The wavelengths corresponding to maximum intensity are 200, 300, and 400 nm respectively. The relation between emissive powers 'E_x', 'E_y' and 'E_z' is E_x > E_y > E_z.

Explanation:

λ_mT = k

`E=(sigmaAT^4)/A`

⇒ E ∝ T⁴

`thereforeEpropA/lambda^4`

E_x : E_y : E_z `=1/lambda_x^4:1/lambda_y^4:1/lambda_z^4=1/200^4:1/300^4:1/400^4`

E_x > E_y > E_z