Time of your life

You're watering the plants in your garden when you notice an atomic bomb has been set off 400 m from your garden. At time $t = 4.3$ ms after the explosion, the fireball is 330 m away.

How much time do you have before you're vaporized by the advancing fireball?

Assumptions

• An insignificant amount of energy is lost to dissipative processes.
• The fireball's advancing front is roughly spherical.
• The surrounding atmosphere has a density of $\rho$ $\mbox{kg/m}^3$ .
• The ambient pressure, in the face of the bomb energy, is completely irrelevant.