A student investigates light from a sodium vapour lamp - Scottish Highers Physics - Question 8 - 2022

The experimental setup is not suitable for investigating the inverse square law because the beam of light does not diverge; it remains parallel regardless of the distance from the collimator to the screen. The inverse square law states that the intensity of light from a point source varies inversely with the square of the distance from the source. Since the light does not spread out, the irradiance remains constant across varying distances in this setup.

Electrons are moving to a lower energy level when this light is emitted.

To calculate the difference in energy (ΔE) between the two energy levels, we can use the formula:

$E = hf$

where:

• $h = 6.63 × 10^{-34} ext{ J·s}$ (Planck’s constant)
• $f = \frac{c}{\lambda}$, where $c = 3.00 × 10^{8} ext{ m/s}$ (speed of light) and $\\lambda = 589.0 × 10^{-9} ext{ m}$ (wavelength)

Calculating the frequency (f):

$f = \frac{3.00 × 10^{8}}{589.0 × 10^{-9}} = 5.08 × 10^{14} ext{ Hz}$

Now substituting back into the energy equation:

$E = (6.63 × 10^{-34}) × (5.08 × 10^{14}) \\E = 3.37 × 10^{-19} ext{ J}$

The student observes a second yellow spectral line at a wavelength of 589.6 nm because there are more electrons (per second) making the transition for the 589.6 nm line than for the 589.0 nm line. This means that more photons of the 589.6 nm wavelength are emitted. Since frequency is related to energy, it does not matter that these photons have a slightly longer wavelength; the electron transitions occur at different rates, affecting the observed brightness.