C

Step 1: Calculate the surface area of the filament.
The filament can be modeled as a cylinder. The surface area (A) of a cylinder is given by:
$$ A = 2 \pi r L $$
where
- r = radius of the filament = 4 \times 10^{-5} \, m
- L = length of the filament = 1.0 \, m

$$ A = 2 \pi (4 \times 10^{-5} \, m)(1.0 \, m) \approx 2.51 \times 10^{-4} \, m^2 $$

Step 2: Use the Stefan-Boltzmann Law.
According to the Stefan-Boltzmann Law, the power radiated by a black body is given by:
$$ P = \varepsilon \sigma A T^4 $$
where
- P = power = 100 \, W
- \varepsilon = emissivity = 0.8
- \sigma = Stefan-Boltzmann constant = 6.0 \times 10^{-8} \, W/m^2 K^4
- T = temperature in Kelvin

Step 3: Rearrange to solve for T.
Rearranging the formula gives:
$$ T^4 = \frac{P}{\varepsilon \sigma A} $$
Substituting in our values:
$$ T^4 = \frac{100 \, W}{0.8 \times 6.0 \times 10^{-8} \, W/m^2 K^4 \times 2.51 \times 10^{-4} \, m^2} $$
Step 4: Calculate T.
Plugging in the numbers:
$$ T^4 = \frac{100}{0.8 \times 6.0 \times 10^{-8} \times 2.51 \times 10^{-4}} \approx 2.518 \times 10^7 \, K^4 $$
Taking the fourth root:
$$ T = (2.518 \times 10^7)^{1/4} \approx 122.45 \, K $$

Therefore, the approximate temperature of the filament when the bulb is operating at correct wattage is around 122.45 K.