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xercise 38.28 7 of 17 Constants PartA A horizontal beam of laser light of wavelength 617 nm passes through a narrow slit that has What is the minimum uncertainty in the vertical component of the momentum of each photon in the beam after the photon has passed through the slit? Express your answer to two significant figures and include the appropriate units width 6.20x10mm. The intensity of the light is measured on a vertical screen that is 2.20 m from the slit. Дру- 8.5x10-31 kg-m Previous Answers Correct Part B Use the result of part A to estimate the width of the central diffraction maximum that is observed on the screen Express your answer to two significant figures and include the appropriate units Templates Symbois undo redo fet keyboard shortcuts help width Previous Answers Request Answer Submit Submitted Answers ANSWER 1 width.044 m ANSWER 2: width4.4 cm ANSWER 3 width4.4.10-2 m ANSWER 4: width44 mm

Answer 1

Part A )

using Heisenberg Uncertainty Principle

$\Delta$x.$\Delta$p $\geq$$\hbar$ / 2

$\Delta$x.$\Delta$p $\approx$$\hbar$ / 2

L . $\Delta$p $\approx$$\hbar$ / 2

$\Delta$p = $\hbar$ / 2 L

= 1.05 x 10^-34 / 2 x 6.2 x 10^-5

$\Delta$p = 8.4677 x 10^-31 kg.m/sec

$\Delta$p = 8.5 x 10^-31 kg.m/sec ( rounded off value )

Part B )

using

W = 2 x $\lambda$ / L

$\Delta$p = $\hbar$ / 2 L

L = $\hbar$ / 2 $\Delta$p

W = 2 x $\lambda$ / $\hbar$ / 2 $\Delta$p

= 4 x $\lambda$$\Delta$p / $\hbar$

= 4 x 2.2 x 617 x 10^-9 x 8.4677 x 10^-31 / 1.05 x 10^-34

W = 0.043786 m

W = 0.044 m ( rounded off value )