The National Ignition Facility has the most powerful laser...

The National Ignition Facility has the most powerful laser in the world; it uses 192 beams to aim $500 .$ TW of power at a spherical pellet of diameter $2.00 \mathrm{~mm} .$ How fast would a pellet of density $2.00 \mathrm{~g} / \mathrm{cm}^{3}$ accelerate if only one of the laser beams hits it for $1.00 \mathrm{~ns}$ and $2.00 \%$ of the light is absorbed?

Key Concepts

Photon Momentum and Radiation Pressure

This concept deals with the fact that light carries momentum, and when it is absorbed or reflected by an object, it exerts a force known as radiation pressure. The relation between energy and momentum for photons is given by E = pc, which allows one to calculate how much momentum is transferred to an object when it absorbs a portion of incident light.

Impulse and Momentum Transfer

Impulse refers to the change in momentum of an object resulting from a force acting over a period of time. In this context, a short burst of laser energy delivers an impulse to the pellet, and by using the relation ?p = F?t, one can find the resulting change in velocity and thereby the acceleration of the pellet.

Mass Determination Using Density and Volume

Calculating the mass of a spherical object from its density and volume is fundamental when applying Newton's laws to find its acceleration. The volume of a sphere is used in conjunction with its density to determine its mass, which is then essential in relating the applied force to the resulting acceleration via Newton's second law.

Newton's Second Law of Motion

Newton's second law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This principle is applied here to connect the force derived from the momentum imparted by the laser (or the radiation pressure) with the acceleration of the pellet.

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