Determine the maximum magnitude of the linear momentum of a...

The energy of the incident photon is given by:

$E = \dfrac{hc}{\lambda} = \dfrac{6.63 \times 10^{-34} \times 3 \times 10^8}{400 \times 10^{-9}} \text{ J} = 4.97 \times 10^{-19} \text{ J}$

The work function of the metal in Joules is:

$\Phi = 2.5 \text{ eV} = 2.5 \times 1.6 \times 10^{-19} \text{ J} = 4.0 \times 10^{-19} \text{ J}$

Using Einstein's photoelectric equation, the maximum kinetic energy of the emitted photoelectron is:

K_{\text\max} = E - \Phi = 4.97 \times 10^{-19} \text{ J} - 4.0 \times 10^{-19} \text{ J} = 0.97 \times 10^{-19} \text{ J}

The maximum magnitude of the linear momentum is related to the maximum kinetic energy by:

p_{\text\max} = \sqrt{2 m_e K_{\text\max}}

Substituting the mass of an electron $m_e = 9.1 \times 10^{-31} \text{ kg}$:

p_{\text\max} = \sqrt{2 \times 9.1 \times 10^{-31} \times 0.97 \times 10^{-19}} \text{ kg m/s}

p_{\text\max} = \sqrt{17.65 \times 10^{-50}} \text{ kg m/s} \approx 4.2 \times 10^{-25} \text{ kg m/s}