What wavelength of light is required to cause the ejection of photoelectrons with kinetic energies of 5.0 *10^-20 J from a calcium surface ($\varPhi$ = 4.60 * 10^-19 J)?

Question

Quizplus · Accepted Answer

The energy required to eject photoelectrons is given by the equation $E = hf = \frac{hc}{\lambda}$, where $E$ is the total energy needed, $h$ is Planck's constant ($6.626 \times 10^{-34} \, \text{m}^2 \, \text{kg} / \text{s}$), $c$ is the speed of light ($3.00 \times 10^8 \, \text{m/s}$), and $\lambda$ is the wavelength of the light. The work function ($\Phi$) of calcium is the minimum energy needed to eject an electron, given as $4.60 \times 10^{-19} \, \text{J}$. The total energy provided by the light must be the sum of the work function and the kinetic energy of the ejected electrons, $E = \Phi + KE$. Substituting the given values, $E = 4.60 \times 10^{-19} \, \text{J} + 5.0 \times 10^{-20} \, \text{J} = 5.10 \times 10^{-19} \, \text{J}$. Solving for $\lambda$ gives a wavelength that corresponds to the option closest to 390 nm.

What Wavelength of Light Is Required to Cause the Ejection Φ\varPhiΦ

What Wavelength of Light Is Required to Cause the Ejection $\varPhi$