Discussion
The minimum energy required to remove an electron from sodium atom is 3.313 × 10-19 J. What is the maximum wavelength of radiation that will eject photoelectron from sodium metal? [h = 6.626 × 10-34 Js]
Answer: E
The maximum wavelength is 600 nm.
The longest wavelength that can eject an electron carries exactly the minimum energy, \(E = \frac{hc}{\lambda}\), with \(c = 3 \times 10^{8}\) m s-1:
\[ \begin{aligned} \lambda &= \frac{hc}{E} = \frac{6.626 \times 10^{-34} \times 3 \times 10^{8}}{3.313 \times 10^{-19}} \\ &= 6 \times 10^{-7}\ \text{m} = 600\ \text{nm} \end{aligned} \]
Since \(6.626 = 2 \times 3.313\), the numbers simplify neatly to \(2 \times 3 \times 10^{-7}\) m. Shorter wavelengths such as 400 or 500 nm would also eject electrons, but they are not the maximum; 700 nm photons carry too little energy.
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