Question

What velocity would a 60 kg person need to move at in order to have the same momentum as a 600 nm photon? (to 2 s.f and in m s−1)

Answer 1

Solution. Photon momentum can be found using the formula

$$p=\frac {h} {\lambda}$$

where h=6.63*10^(-34) J*s; lambda=600*10^(-9)m  is the photon's wavelength.

Human impulse can be found using the formula

$$p=mv$$

where m=60kg is mass of person; v is velocity. Therefore

$$\frac {h} {\lambda}=mv \Longrightarrow v= \frac {h} {\lambda m}.$$

Hence

$$v= \frac {6.63 \times 10^{-34} } {600 \times 10^{-9} \times 60}=1.84 \times 10^{-29} \frac {m} {s}$$

Answer.

$$1.84 \times 10^{-29} \frac {m} {s}$$