a minimum of 414.8 kj/mol is required to remove an electron from a(n) zinc metal surface. what is the…

Explanation:

Step1: Convert energy per mole to energy per photon

First, convert the energy required per mole ($414.8\ kJ/mol$) to energy per photon. Use Avogadro's number ($N_A = 6.022\times 10^{23}\ mol^{-1}$). $E=\frac{414.8\times10^{3}\ J/mol}{6.022\times 10^{23}\ mol^{-1}}$ $E\approx 6.89\times 10^{-19}\ J$

Step2: Use the energy - wavelength relation

The energy of a photon is given by $E = h\nu=\frac{hc}{\lambda}$, where $h = 6.626\times 10^{-34}\ J\cdot s$ is Planck's constant, $c = 3\times 10^{8}\ m/s$ is the speed of light, and $\lambda$ is the wavelength. We can re - arrange the formula for $\lambda$: $\lambda=\frac{hc}{E}$. Substitute $h = 6.626\times 10^{-34}\ J\cdot s$, $c = 3\times 10^{8}\ m/s$ and $E = 6.89\times 10^{-19}\ J$ into the formula. $\lambda=\frac{6.626\times 10^{-34}\ J\cdot s\times3\times 10^{8}\ m/s}{6.89\times 10^{-19}\ J}$ $\lambda\approx 2.89\times 10^{-7}\ m$

Step3: Convert wavelength to nanometers

Since $1\ m=10^{9}\ nm$, then $\lambda = 2.89\times 10^{-7}\ m\times10^{9}\ nm/m = 289\ nm$

Answer:

289