Question

Determine the wavelengths and frequencies for photons with energies

1. \[10^{-12}\mathrm{J}\],
2. \[10^{-15}\mathrm{J}\],
3. \[10^{-18}\mathrm{J}\],
4. \[10^{-21}\mathrm{J}\] and
5. \[10^{-24}\mathrm{J}\].

Arrange the electromagnetic-spectrum regions along a horizontal line.

Answer 1

Use \[\nu = \frac{E}{h}\] and \[\lambda = \frac{c}{\nu} = \frac{hc}{E}\], with \[h = 6.626 \times 10^{-34},\mathrm{J,s}\] and \[c = 3.00 \times 10^{8},\mathrm{m,s^{-1}}].

Photon energy	Frequency	Wavelength	Approximate region
\[10^{-12}\mathrm{J}\]	\[1.51 \times 10^{21}\mathrm{Hz}\]	\[1.99 \times 10^{-13}\mathrm{m}\]	Gamma rays
\[10^{-15}\mathrm{J}\]	\[1.51 \times 10^{18}\mathrm{Hz}\]	\[1.99 \times 10^{-10}\mathrm{m}\]	X-rays
\[10^{-18}\mathrm{J}\]	\[1.51 \times 10^{15}\mathrm{Hz}\]	\[1.99 \times 10^{-7}\mathrm{m}\]	Ultraviolet
\[10^{-21}\mathrm{J}\]	\[1.51 \times 10^{12}\mathrm{Hz}\]	\[1.99 \times 10^{-4}\mathrm{m}\]	Infrared/submillimetre
\[10^{-24}\mathrm{J}\]	\[1.51 \times 10^{9}\mathrm{Hz}\]	\[1.99 \times 10^{-1}\mathrm{m}\]	Radio-frequency region (microwave band)

Spectrum arranged from shorter to longer wavelength:

Gamma rays → X-rays → Ultraviolet → Visible light → Infrared → Microwaves → Radio waves

Moving left to right, wavelength increases while frequency and photon energy decrease. The precise boundaries between spectrum regions are approximate.