| List-I EM-Wave | List-II Wavelength Range |
|---|---|
| (A) Infra-red | (III) 1 mm to 700 nm |
| (B) Ultraviolet | (II) 400 nm to 1 nm |
| (C) X-rays | (IV) 1 nm to \(10^{-3}\) nm |
| (D) Gamma rays | (I) \(<10^{-3}\) nm |
The correct matching between the EM waves and their wavelength ranges is as follows:
- (A) Infra-red corresponds to \( 1 \, \text{mm} \) to \( 700 \, \text{nm} \), which is (III).
- (B) Ultraviolet corresponds to \( 400 \, \text{nm} \) to \( 1 \, \text{nm} \), which is (II).
- (C) X-rays correspond to \( 1 \, \text{nm} \) to \( 10^{-3} \, \text{nm} \), which is (IV).
- (D) Gamma rays correspond to wavelengths less than \( 10^{-3} \, \text{nm} \), which is (I).
Thus, the correct matching is:
\[ \text{(A)-(III), (B)-(II), (C)-(IV), (D)-(I)} \]
Infrared radiation has the longest wavelength among the options, while gamma rays have the shortest wavelength, corresponding to their relative energy levels, with gamma rays being the most energetic and infrared the least.
A black body is at a temperature of 2880 K. The energy of radiation emitted by this body with wavelength between 499 nm and 500 nm is U1, between 999 nm and 1000 nm is U2 and between 1499 nm and 1500 nm is U3. The Wien's constant, b = 2.88×106 nm-K. Then,

What will be the equilibrium constant of the given reaction carried out in a \(5 \,L\) vessel and having equilibrium amounts of \(A_2\) and \(A\) as \(0.5\) mole and \(2 \times 10^{-6}\) mole respectively?
The reaction : \(A_2 \rightleftharpoons 2A\)