a ruby laser emits light at wavelength 694.4nm. if a laser pulse is emitted for 12pico seconds and the energy released per pulse is 100mJ, what is the length of the pulse?

To find the length of the pulse, we need to calculate the speed of light first. The speed of light (c) is approximately 3.00 x 10^8 meters per second.

Next, we convert the wavelength from nanometers (nm) to meters (m). There are 1 x 10^9 nm in a meter, so the wavelength of the ruby laser is 694.4 x 10^-9 meters.

Now, we can calculate the frequency (f) of the laser pulse using the equation:

c = f * λ

Where:
c = speed of light
f = frequency
λ = wavelength

Rearranging the equation to solve for frequency:

f = c / λ

Plugging in the values:

f = (3.00 x 10^8 m/s) / (694.4 x 10^-9 m)
f ≈ 4.32 x 10^14 Hz

Now, we have the frequency of the laser pulse.

To find the length of the pulse, we divide the given duration by the frequency:

pulse length = 12 picoseconds / (4.32 x 10^14 Hz)

Since a picosecond (ps) is 10^-12 seconds, we convert it to seconds:

pulse length = 12 x 10^-12 seconds / (4.32 x 10^14 Hz)

Next, simplify the units:

pulse length = 12 x 10^-12 / 4.32 x 10^14 seconds

Divide the numerator and denominator by 12:

pulse length ≈ 10^-12 / 3.60 x 10^14 seconds

Convert the denominator to scientific notation:

pulse length ≈ 2.78 x 10^-27 seconds

Therefore, the length of the pulse is approximately 2.78 x 10^-27 seconds.