A light-emitting diode (LED) emits light over a narrow range of wavelengths. These wavelengths are distributed about a peak wavelength $ \lambda_p $. Two LEDs $ L_G $ and $ L_R $ are adjusted to give the same maximum light intensity. $ L_G $ emits green light and $ L_R $ emits red light. Figure 3 shows how the light output of the LEDs varies with the wavelength $ \lambda $. Light from $ L_R $ is incident normally on a plane diffraction grating. The fifth-order maximum for light of wavelength $ \lambda_p $ occurs at a diffraction angle of 76.3º. Determine $ N $, the number of lines per metre on the grating. Suggest one possible disadvantage of using the fifth-order maximum to determine $ N $. Figure 4 shows part of the current–voltage characteristics for $ L_R $ and $ L_G $. When the linear part of the characteristic is extrapolated, the point at which it meets the horizontal axis gives the activation voltage $ V_A $ for the LED. $ V_A $ for $ L_G $ is 2.00 V. Determine, using Figure 4, $ V_A $ for $ L_R $. It can be shown that $ V_A = \frac{hc}{e\lambda_p} $, where $ h $ is the Planck constant. Deduce a value for the Planck constant based on the data given about the LEDs. Figure 5 shows a circuit with $ L_R $ connected to a resistor of resistance $ R $. The power supply has emf 6.10 V and negligible internal resistance. The current in $ L_R $ must not exceed 21.0 mA. Deduce the minimum value of $ R $.

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A light-emitting diode (LED) emits light over a narrow range of wavelengths - AQA - A-Level Physics - Question 2 - 2021 - Paper 3

Question 2

A light-emitting diode (LED) emits light over a narrow range of wavelengths. These wavelengths are distributed about a peak wavelength $ \lambda_p $. Two LEDs \( ... show full transcript

Worked Solution & Example Answer:A light-emitting diode (LED) emits light over a narrow range of wavelengths - AQA - A-Level Physics - Question 2 - 2021 - Paper 3

Step 1

Determine N, the number of lines per metre on the grating.

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Answer

To find the number of lines per metre, we can use the formula for diffraction at the nth order:

$d \sin(\theta) = n\lambda,$

where:

( d ) = distance between adjacent grating lines (reciprocal of N)
( \theta = 76.3º )
( n = 5 ) (fifth order)
( \lambda = \lambda_p ) (green LED wavelength).

Rearranging gives: $N = \frac{1}{d} = \frac{n}{\lambda \sin(\theta)}$ .

Substituting values:

Using the approximate wavelength ( \lambda \approx 550 ) nm (green light) gives:

$N = \frac{5}{550 \times 10^{-9} \times \sin(76.3º)} \approx 3.06 \times 10^6 \text{ lines/m}.$

Step 2

Suggest one possible disadvantage of using the fifth-order maximum to determine N.

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Answer

One possible disadvantage is that the fifth-order maximum may be less pronounced or fainter, making it harder to measure accurately compared to lower order maxima, which could result in less reliable data.

Step 3

Determine, using Figure 4, VA for LR.

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Answer

From the linear region of the ( L_R ) characteristic, we can extrapolate to find the activation voltage ( V_A ).

It appears from the graph that ( V_A \approx 1.85 V ) for the red LED ( L_R ).

Step 4

Deduce a value for the Planck constant based on the data given about the LEDs.

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Answer

Using the formula for the activation voltage:

$V_A = \frac{hc}{e\lambda_p},$

Where:

( V_A ) is known for ( L_G ) (2.00 V).
Using a wavelength of approximately 550 nm for green light: ( \lambda_p = 550 \times 10^{-9} ) m.
Using the charge of an electron ( e \approx 1.6 \times 10^{-19} ) C.

Rearranging to find ( h ):

$h = \frac{V_A e \lambda_p}{c} = \frac{2.00 \times (1.6 \times 10^{-19}) \times (550 \times 10^{-9})}{3.00 \times 10^8}$

Calculating gives:

$h \approx 6.63 \times 10^{-34} \text{ J s}.$

Step 5

Deduce the minimum value of R.

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Answer

Using Ohm's law and the power supply specifications:

The voltage across the resistor is: $V_R = V_{source} - V_A = 6.10 - 2.00 = 4.10 V.$

The maximum current through ( L_R ) is 21.0 mA:

$I_{max} = 0.021 A.$

Using Ohm's law to find resistance: $R = \frac{V_R}{I_{max}} = \frac{4.10}{0.021} \approx 195.24 \Omega.$

Thus, the minimum value of ( R ) should be rounded up to 196 Ω.

A light-emitting diode (LED) emits light over a narrow range of wavelengths - AQA - A-Level Physics - Question 2 - 2021 - Paper 3

Worked Solution & Example Answer:A light-emitting diode (LED) emits light over a narrow range of wavelengths - AQA - A-Level Physics - Question 2 - 2021 - Paper 3

Determine N, the number of lines per metre on the grating.

Suggest one possible disadvantage of using the fifth-order maximum to determine N.

Determine, using Figure 4, VA for LR.

Deduce a value for the Planck constant based on the data given about the LEDs.

Deduce the minimum value of R.

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