What is the intensity in W/m2 of a laser beam used to burn away cancerous tissue that, when 91.0% absorbed, puts 540 J of energy into a circular spot 2.60 mm in diameter in 4.00 s?

2.3x10⁷ W/m²

Explanation:

The intensity (I) of a laser is its potency (P) divided by the area (A) that it is affected. The potency is the energy applied (or absorbed) in a period, thus id 91.0% of the energy is absorbed, so:

E = 0.91*540 = 491.4 J

And,

P = E/t, where t is the time in seconds

P = 491.4/4.00

P = 122.85 J/s

P = 122.85 W

The are of a circular spot is:

A = (π/4) * d²

Where d is the diameter. Thus, with d = 2.60 mm = 0.0026 m

A = (π/4) * (0.0026) ²

A = 5.31x10⁻⁶ m²

I = P/A

I = 122.85/5.31x10⁻⁶

I = 2.3x10⁷ W/m²