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Dispersion coefficients at \( 1 \) km are \( \sigma_y = 150 \) m and \( \sigma_z = 90 \) m. The product \( \pi \sigma_y \sigma_z \) is about

  • A.240 m\(^2\)
  • B.84800 m\(^2\)
  • C.42400 m\(^2\)
  • D.13500 m\(^2\)

Answer: C

Correct answer: 42400 m\(^2\)

Substituting the two dispersion coefficients:

\[ \pi \sigma_y \sigma_z = \pi \times 150 \times 90 = \pi \times 13500 \approx 42412\ \text{m}^2 \]

which rounds to about \( 42400 \). The distractor \( 13500 \) is the product without \( \pi \), and \( 84800 \) doubles the result - the factor of two belongs in the full expression \( 2\pi u \sigma_y \sigma_z \), not in this product. The quantity has the character of an effective cross-sectional area over which the emission is spread.

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