A person is standing at the side of a road - Scottish Highers Physics - Question 5 - 2023

The frequency of the sound heard by the person as the police car moves away is less than the frequency heard when the car was approaching. This is due to the Doppler effect where the apparent frequency decreases as the source moves away. The waves are stretched, resulting in a longer wavelength and lower frequency.

The period (T) of the AC supply can be calculated using the formula:

$T = \frac{1}{f}$

Given that the red and blue LEDs flash twice per second, the frequency (f) is 2 Hz. Therefore:

$T = \frac{1}{2} = 0.5 s.$

Thus, the period of the AC supply used is 0.5 seconds.

The red LEDs and blue LEDs do not light at the same time because they are connected in different configurations regarding their biasing. LED operation requires a forward bias to conduct, hence, when one color LED is forward biased, the other is reverse biased. This results in alternating light emission between the two colors at different instances.

To determine the energy of the emitted photon, we use the equation:

$E = hf$

Where:

• $E$ is the energy of the photon.
• $h$ is Planck's constant ($6.63 \times 10^{-34}$ J s).
• $f$ is the frequency of the photon, which can be calculated using the speed of light ($c$) and wavelength ($\lambda$):

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

Given:

• $\lambda = 625 nm = 625 \times 10^{-9} m$,
• $c = 3.00 \times 10^8 m/s$,

We calculate:

$f = \frac{3.00 \times 10^8}{625 \times 10^{-9}} \approx 4.8 \times 10^{14} Hz.$

Now, substituting back into the energy formula:

$E = (6.63 \times 10^{-34}) (4.8 \times 10^{14}) \approx 3.18 \times 10^{-19} J.$

Therefore, the energy of the emitted photon is approximately $3.18 \times 10^{-19} J.$

The difference between the red LEDs and blue LEDs lies in their energy band gaps. Red LEDs have a larger band gap compared to blue LEDs, meaning they emit light at longer wavelengths (lower energy). In contrast, blue LEDs have a smaller band gap, allowing them to emit light at shorter wavelengths (higher energy). This inherent difference in energy gap correlates with the energy of the emitted photons, with blue light containing more energy than red light.