Ac cording to Stefan' law of radiation, a black body radiates energy `sigma T^4` from its unit surface area every second where T is the surface temperature of the black body and `sigma = 5.67 xx 10^(-8) W//m^2 K^4` is known as Stefan's constant. A nuclear weapon may be thought of as a ball of radius 0.5 m When detoneted, it reachs temperature of `10^6 K` and can be treated as a black body. (a) Estimate the power it radiates. (b) if surrounding has water at `30^@C` how much water can 10% of the energy produced evaporate in 1s ? ` [s_w = 4186.0 J//Kg K and L_(upsilon) = 22.6 xx 10^5 J//kg]` (c ) If all this energy U is in the form of radiation, corresponding momentum is ` p = U//c.` How much momentum per unit time does it impart on unit area at a distance of 1 km ?

Explanation

Let's solve the question step by step.

### Given Data:
- Radius of the nuclear weapon (black body), \( r = 0.5 \, \text{m} \)
- Temperature, \( T = 10^6 \, \text{K} \)
- Stefan's constant, \( \sigma = 5.67 \times 10^{-8} \, \text{W/m}^2 \text{K}^4 \)
- Specific heat of water, \( s_w = 4186.0 \, \text{J/kg K} \)
- Latent heat of vaporization, \( L_v = 22.6 \times 10^5 \, \text{J/kg} \)
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