Question

the work function energy for lithium is $3.64 \times 10^{-19}$ j. what is the longest wavelength of the radiation that could eject an electron from lithium? ? nm

Explanation:

Step1: Recall photoelectric work function formula

The work function $W$ equals the photon energy at threshold: $W = h
u = \frac{hc}{\lambda}$, where $h=6.626\times10^{-34}\ \text{J·s}$, $c=3.00\times10^8\ \text{m/s}$, $\lambda$ is wavelength.

Step2: Rearrange for wavelength

$\lambda = \frac{hc}{W}$

Step3: Substitute given values

$\lambda = \frac{(6.626\times10^{-34}\ \text{J·s})(3.00\times10^8\ \text{m/s})}{3.64\times10^{-19}\ \text{J}}$

Step4: Calculate and convert to nm

First compute in meters: $\lambda \approx 5.46\times10^{-7}\ \text{m}$. Convert to nm: $5.46\times10^{-7}\ \text{m} \times 10^9\ \text{nm/m} = 546\ \text{nm}$

Answer:

546 nm