Answer:
10⁻⁶
Step-by-step explanation:
Since the volume of saliva coughed up by my friend is 0.0100 cm³ and 10⁺⁹ of this volume contains the virus. The volume containing the virus is thus V = 0.0100 cm³ × 10⁺⁹ = 0.0100 × 10⁺⁹ cm³ = 0.0100 × 10⁺⁹ × 10⁻⁶ m³ = 0.0100 × 10⁺¹⁵ m³.
Now, since the flu virus is spherical, its volume is v = 4πr³/3 where r is its radius.
Let n flu viruses be contained in the volume V of flu viruses coughed out by my friend.
So n × v = V
v = V/n
4πr³/3 = V/n
r = ∛(3V/4πn)
substituting the value of V into the equation, we have
r = ∛(3 × 0.0100 × 10⁺¹⁵ m³/4πn)
r = (∛0.03/4πn) × 10⁻⁵ m
r = 0.1336/∛n × 10⁻⁵ m
r = 1.336/∛n × 10⁻⁶ m
Since the factor 10⁻⁶ is found in the radius, the order of magnitude of the influenza virus that have just landed on me are of the order 10⁻⁶
