A laser that emits pulses of UV lasting 2.95 ns has a beam diameter of 4.05 mm. If each burst contains an energy of 4.60 J, what is the length in space of each pulse?
What is the average energy per unit volume (the energy density) in one of these pulses?
To find the length in space of each pulse, we need to determine the speed at which the pulse is propagating. We know that the speed of light in a vacuum, denoted by "c," is approximately 299,792,458 meters per second (m/s).
Given that the pulse lasts for 2.95 ns, or 2.95 x 10^(-9) seconds, and the beam diameter is 4.05 mm, or 4.05 x 10^(-3) meters, we can use the formula:
Length = Speed x Time
First, let's convert the beam diameter to meters:
Diameter = 4.05 mm = 4.05 x 10^(-3) meters
Now, we can calculate the speed of the pulse:
Speed = c = 299,792,458 m/s
Length = Speed x Time
Length = (299,792,458 m/s) x (2.95 x 10^(-9) s)
Length ≈ 883.823 meters
Therefore, the length in space of each pulse is approximately 883.823 meters.
Moving on to finding the average energy per unit volume (energy density) in one of these pulses, we can use the formula:
Energy Density = Energy / Volume
The energy per pulse is given as 4.60 J, and the volume can be calculated using the formula for the volume of a cylinder:
Volume = π x (radius^2) x length
Since the beam diameter is given, we can calculate the radius (r) by dividing it by 2:
Radius = 4.05 mm / 2 = 2.025 mm = 2.025 x 10^(-3) meters
Now we can find the volume:
Volume = π x (2.025 x 10^(-3) meters)^2 x 883.823 meters
Volume ≈ 11.575 x 10^(-9) cubic meters
Finally, we can calculate the energy density:
Energy Density = 4.60 J / 11.575 x 10^(-9) cubic meters
Energy Density ≈ 396.975 x 10^9 J/m^3
Therefore, the average energy per unit volume (the energy density) in one of these pulses is approximately 396.975 x 10^9 J/m^3.