Final Momentum of Object Absorbing a Light Pulse

To find the final momentum acquired by the object, we can use the relationship between the energy of electromagnetic radiation and its momentum.

1. Given Data:

• Duration of the radiation pulse, $\Delta t = 100\text{ ns} = 100 \times 10^{-9}\text{ s} = 10^{-7}\text{ s}$
• Power delivered by the pulse, $P = 30\text{ mW} = 30 \times 10^{-3}\text{ W} = 3 \times 10^{-2}\text{ W}$
• Speed of light, $c = 3 \times 10^8\text{ ms}^{-1}$

2. Calculation of Total Energy Delivered: The total energy $E$ contained in the pulse is given by: $E = P \times \Delta t$

Substituting the given values: $E = (30 \times 10^{-3}\text{ W}) \times (100 \times 10^{-9}\text{ s})$ $E = 3 \times 10^{-9}\text{ J}$

3. Calculation of Momentum Acquired: When electromagnetic radiation of energy $E$ is completely absorbed by an object initially at rest, the momentum $p$ transferred to the object is given by Einstein's mass-energy-momentum relation for photons: $p = \frac{E}{c}$

Substituting $E$ and $c$: $p = \frac{3 \times 10^{-9}\text{ J}}{3 \times 10^8\text{ ms}^{-1}}$ $p = 1.0 \times 10^{-17}\text{ kg ms}^{-1}$

Therefore, the resulting momentum acquired by the object is $1.0 \times 10^{-17}\text{ kg ms}^{-1}$.

Correct Option: B