We think you are located in South Africa. Is this correct?

Test yourself now

High marks in science are the key to your success and future plans. Test yourself and learn more on Siyavula Practice.

Exercise 12.3

Calculate the energy of a photon of red light with a wavelength of $$\text{400}$$ $$\text{nm}$$.

We first calculate the energy of the photons:

\begin{align*} E & = \frac{hc}{\lambda}\\ & = \frac{(\text{3} \times \text{10}^{\text{8}})(\text{6,63} \times \text{10}^{-\text{34}})}{\text{400} \times \text{10}^{-\text{9}}}\\ & = \text{2,01} \times \text{10}^{-\text{19}}\text{ J} \end{align*}

Next convert the work function energy into J:

\begin{align*} \text{2,9} \times \text{1,6} \times \text{10}^{-\text{19}} = \text{4,64} \times \text{10}^{-\text{19}}\text{ J} \end{align*}

The energy of the photons is less than the work function of calcium and so no electrons will be emitted.

Will ultraviolet light with a wavelength of $$\text{990}$$ $$\text{nm}$$ be able to emit electrons from a sheet of calcium with a work function of $$\text{2,9}$$ $$\text{eV}$$?

\begin{align*} E & = \frac{hc}{\lambda}\\ & = \frac{(\text{3} \times \text{10}^{\text{8}})(\text{6,63} \times \text{10}^{-\text{34}})}{\text{990} \times \text{10}^{-\text{9}}}\\ & = \text{4,97} \times \text{10}^{-\text{19}}\text{ J} \end{align*}