The work function of a certain metal is $1.90 \mathrm { eV }$. What is the longest wavelength of light that can cause photoelectron emission from this metal? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times \right.$ 10^-34 J.s) A) $14.0 \mathrm {~nm}$ B) $62.4 \mathrm {~nm}$ C) $654 \mathrm {~nm}$ D) $231 \mathrm {~nm}$ E) $344 \mathrm {~nm}$

Question

The work function of a certain metal is $1.90 \mathrm { eV }$. What is the longest wavelength of light that can cause photoelectron emission from this metal? $\left( 1 \mathrm { eV } = 1.60 \times 10 ^ { - 19 } \mathrm {~J} , c = 3.00 \times 10 ^ { 8 } \mathrm {~m} / \mathrm { s } , h = 6.626 \times \right.$ 10>^-34 J.s) A) $14.0 \mathrm {~nm}$ B) $62.4 \mathrm {~nm}$ C) $654 \mathrm {~nm}$ D) $231 \mathrm {~nm}$ E) $344 \mathrm {~nm}$

Quizplus · Accepted Answer

The energy of the photon must be equal to or greater than the work function to emit photoelectrons. Using $E = \frac{hc}{\lambda}$, where $E = 1.90 \, \text{eV} = 3.04 \times 10^{-19} \, \text{J}$, we solve for $\lambda$: $\lambda = \frac{hc}{E} = \frac{6.626 \times 10^{-34} \times 3.00 \times 10^8}{3.04 \times 10^{-19}} \approx 654 \, \text{nm}$.

The Work Function of a Certain Metal Is 1.90eV1.90 \mathrm { eV }1.90eV

The Work Function of a Certain Metal Is $1.90 \mathrm { eV }$