Question

A typical virus is a packet of protein and DNA (or RNA) and can be spherical in shape. The influenza A virus is a spherical virus that has a diameter of 89.2 nm. If the volume of saliva coughed onto you by your friend with the flu is 0.0100 cm3 and 10−9 is the fraction of that volume that consists of viral particles, what is the order of magnitude of the influenza viruses that have just landed on you?

Answer 1

10⁻⁶

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