In a physics laboratory, a diffraction grating with 400 lines per millimetre400\text{ lines per millimetre}400 lines per millimetre is aligned in front of a light source. A student looks through the grating at a ruler placed parallel to the grating at a distance of 1.20 m1.20\text{ m}1.20 m.
A first-order bright red line is observed on the ruler at a position x=32 cmx = 32\text{ cm}x=32 cm from the central zero-order maximum.
Show that the energy of a photon of wavelength 640 nm640\text{ nm}640 nm is approximately 3.11×10−19 J3.11 \times 10^{-19}\text{ J}3.11×10−19 J.
Figure 1 shows some of the energy levels of an electron in this atom.
Identify the initial and final energy levels (in 10−19 J10^{-19}\text{ J}10−19 J) for the electron transition that would cause the emission of a photon of wavelength 640 nm640\text{ nm}640 nm.
