Chapter 6, Problem 6.89PAE

6.101 Laser welding is a technique in which a tightly focused laser beam is used to deposit enough energy to weld metal parts together. Because the entire process can be automated, it is commonly used in many large-scale industries, including the manufacture of automobiles. In order to achieve the desired weld quality, the steel parts being joined must absorb energy at a rate of about 10⁴ W/mm². (Recall that 1 W = 1 J/s.) A particular laser welding system employs a Nd:YAG laser operating at a wavelength of $1.06\mu m$ ; at this wavelength steel will absorb about 80% of the incident photons. If the laser beam is focused to illuminate a circular spot with a diameter of 0.02 inch, what is the minimum power (in watts) that the laser must emit to reach the 10⁴ W/mm² threshold? How many photons per second does this correspond to? (For simplicity, assume that the energy from the laser does not penetrate into the metal to any significant depth.)