Light from a yellow-orange semiconductor diode (LYL_{\text{Y}}LY) is incident normally on a plane diffraction grating. The peak wavelength of the emitted light is λp=590 nm\lambda_{\text{p}} = 590 \text{ nm}λp=590 nm. The second-order maximum (n=2n=2n=2) for this wavelength occurs at a diffraction angle of 42.8∘42.8^\circ42.8∘.
Determine NNN, the number of lines per metre on the grating.
Suggest one possible disadvantage of using a higher-order maximum, such as the second-order maximum, to determine NNN with an LED light source.
The relationship between the activation voltage VAV_{\text{A}}VA of the LED and its peak wavelength λp\lambda_{\text{p}}λp is given by:
VA=hceλp V_{\text{A}} = \frac{hc}{e\lambda_{\text{p}}} VA=eλphcCalculate the activation voltage VAV_{\text{A}}VA for this LED. (Take h=6.63×10−34 J sh = 6.63 \times 10^{-34} \text{ J s}h=6.63×10−34 J s, c=3.00×108 m s−1c = 3.00 \times 10^8 \text{ m s}^{-1}c=3.00×108 m s−1, and e=1.60×10−19 Ce = 1.60 \times 10^{-19} \text{ C}e=1.60×10−19 C).
The LED is connected in series with a resistor of resistance RRR across a power supply of emf 9.00 V9.00 \text{ V}9.00 V and negligible internal resistance. The current must not exceed 12.5 mA12.5 \text{ mA}12.5 mA. At this current, the potential difference across the LED is 2.18 V2.18 \text{ V}2.18 V. Determine the minimum value of RRR.
