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 as expected from a point source. In ideal conditions, as the distance from a point source increases, the intensity would decrease with the square of the distance. However, since a collimator produces a parallel beam, the irradiance remains constant regardless of distance changes, violating the premise of the inverse square relationship.

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

The energy of a photon is given by the equation:

$E = hf$

Where:

• $E$ is the energy of the photon
• $h$ is Planck’s constant ($6.63 \times 10^{-34} ext{ J s}$)
• $f$ is the frequency of the light.

To find the frequency, we can use the relation:

$f = \frac{c}{\lambda}$

Where:

• $c$ is the speed of light ($3.00 \times 10^{8} ext{ m/s}$)
• $\lambda$ is the wavelength ($589.0 \text{ nm} = 589.0 \times 10^{-9} ext{ m}$).

Calculating the frequency:

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

Now, substituting $f$ to find the energy:

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

The student observes a second yellow spectral line at a wavelength of 586.9 nm because there are more electrons (per second) making the transition for the 586.9 nm line. This indicates that either more photons are emitted or that fewer electrons make transitions to higher energy levels, resulting in a brighter line due to increased photon energy.