Two spherical bodies of same materials having radii 0.2 m and 0.8 m are placed in same atmosphere. The temperature of the smaller body is 800 K and temperature of the bigger body is 400 K . If the energy radiated from the smaller body is E, the energy radiated from the bigger body is (assume, effect of the surrounding temperature to be negligible),

We need to find the energy radiated from the bigger body given information about two spherical bodies.

The energy radiated per unit time by a body is given by Stefan's law:

$$E = \sigma A T^4$$

where $$A = 4\pi r^2$$ is the surface area.

For the smaller body: $$r_1 = 0.2$$ m, $$T_1 = 800$$ K

$$E_1 = \sigma \times 4\pi (0.2)^2 \times (800)^4 = E$$

For the bigger body: $$r_2 = 0.8$$ m, $$T_2 = 400$$ K

$$E_2 = \sigma \times 4\pi (0.8)^2 \times (400)^4$$

$$\frac{E_2}{E_1} = \frac{(0.8)^2 \times (400)^4}{(0.2)^2 \times (800)^4}$$

$$= \frac{(0.8)^2}{(0.2)^2} \times \frac{(400)^4}{(800)^4}$$

$$= \left(\frac{0.8}{0.2}\right)^2 \times \left(\frac{400}{800}\right)^4$$

$$= 4^2 \times \left(\frac{1}{2}\right)^4$$

$$= 16 \times \frac{1}{16} = 1$$

Therefore, $$E_2 = E$$.

The correct answer is Option 2: E.