PHYSICS
PHYSICS
5th Edition
ISBN: 2818440038631
Author: GIAMBATTISTA
Publisher: MCG
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Chapter 28, Problem 81P
To determine

The slit width.

Expert Solution & Answer
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Answer to Problem 81P

The slit width is 352×109m.

Explanation of Solution

The width of the central maximum is 1.13mm, slit-screen distance is 1.0m and the accelerating potential difference is 38.0 V.

Write the expression for de Broglie wavelength

λ=hmv                                           (I)

Here, λ is the de Broglie wavelength, h is the Planck’s constant, m is the mass of the electron and v is its velocity.

Write the expression for kinetic energy

K=12mv2                                           (II)

Here, K is the kinetic energy of the electron.

Rearranging the above equation

v=2Km                                           (III)

Substituting (III) in (I)

λ=hmm2K

λ=h2mK                                           (IV)

Write the expression for kinetic energy in terms of accelerating potential

K=eV                                            (V)

Here e is the charge of the electron and V is the accelerating potential difference.

Substituting (V) in (VI)

λ=h2meV                                           (VI)

Write the expression for first diffraction minima

sinθ=λa                                                                    (VII)

Here, θ is the angle of first diffraction minima, λ is the wavelength and a is the slit width.

Using small angle approximation i.e. sinθθ in (VII) and rearranging

λ=θa                                                                    (VIII)

Write the angle of diffraction (refer figure 1)

PHYSICS, Chapter 28, Problem 81P

tanθ=xD                                                                     (IX)

Here, x is half the width of the central maximum, D is the slit-screen distance

Using small angle approximation i.e. tanθθ in (IX)

θ=xD                                                                     (X)

Substituting (X) in (VIII)

λ=xDa                                                                    (XI)

Equating (IV) and (IX)

h2meV=xDa

Rearranging for a

  a=hDx2meV                                                                 (XII)

Substitute 9.109×1031 kg for m, 1.00 m for D, 38 V for V, 1.13mm/2 for x and 6.626×1034 Js for h in (XII) to find a

a=6.626×1034 Js×1.00 m(1.13mm/2)2×9.109×1031 kg×38.0 eV=6.626×1034 Js×1.00 m(0.565×103m)2×9.109×1031 kg×38.0 eV×1.602×1019 J=352×109m=352nm

Thus, the slit width is 352×109m.

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Chapter 28 Solutions

PHYSICS

Ch. 28 - Prob. 2CQCh. 28 - Prob. 3CQCh. 28 - Prob. 4CQCh. 28 - Prob. 5CQCh. 28 - Prob. 6CQCh. 28 - Prob. 7CQCh. 28 - Prob. 8CQCh. 28 - Prob. 9CQCh. 28 - Prob. 10CQCh. 28 - Prob. 11CQCh. 28 - Prob. 12CQCh. 28 - Prob. 13CQCh. 28 - Prob. 14CQCh. 28 - Prob. 15CQCh. 28 - Prob. 16CQCh. 28 - Prob. 17CQCh. 28 - Prob. 18CQCh. 28 - Prob. 1MCQCh. 28 - Prob. 2MCQCh. 28 - Prob. 3MCQCh. 28 - Prob. 4MCQCh. 28 - Prob. 5MCQCh. 28 - Prob. 6MCQCh. 28 - Prob. 7MCQCh. 28 - Prob. 8MCQCh. 28 - Prob. 9MCQCh. 28 - Prob. 10MCQCh. 28 - Prob. 1PCh. 28 - Prob. 2PCh. 28 - Prob. 3PCh. 28 - Prob. 4PCh. 28 - Prob. 5PCh. 28 - Prob. 6PCh. 28 - Prob. 7PCh. 28 - Prob. 8PCh. 28 - Prob. 9PCh. 28 - Prob. 10PCh. 28 - Prob. 11PCh. 28 - Prob. 12PCh. 28 - Prob. 13PCh. 28 - Prob. 15PCh. 28 - Prob. 14PCh. 28 - Prob. 17PCh. 28 - Prob. 16PCh. 28 - Prob. 18PCh. 28 - Prob. 19PCh. 28 - Prob. 20PCh. 28 - Prob. 21PCh. 28 - Prob. 23PCh. 28 - Prob. 22PCh. 28 - Prob. 25PCh. 28 - Prob. 24PCh. 28 - Prob. 26PCh. 28 - Prob. 27PCh. 28 - Prob. 28PCh. 28 - Prob. 29PCh. 28 - Prob. 30PCh. 28 - Prob. 32PCh. 28 - Prob. 31PCh. 28 - Prob. 33PCh. 28 - Prob. 34PCh. 28 - Prob. 35PCh. 28 - Prob. 36PCh. 28 - Prob. 37PCh. 28 - Prob. 39PCh. 28 - Prob. 41PCh. 28 - Prob. 40PCh. 28 - Prob. 38PCh. 28 - Prob. 42PCh. 28 - Prob. 43PCh. 28 - Prob. 44PCh. 28 - Prob. 45PCh. 28 - Prob. 46PCh. 28 - Prob. 47PCh. 28 - Prob. 48PCh. 28 - Prob. 49PCh. 28 - Prob. 50PCh. 28 - Prob. 51PCh. 28 - Prob. 52PCh. 28 - Prob. 53PCh. 28 - Prob. 54PCh. 28 - Prob. 55PCh. 28 - Prob. 56PCh. 28 - Prob. 57PCh. 28 - Prob. 58PCh. 28 - Prob. 59PCh. 28 - Prob. 60PCh. 28 - Prob. 61PCh. 28 - Prob. 62PCh. 28 - Prob. 63PCh. 28 - Prob. 65PCh. 28 - Prob. 64PCh. 28 - Prob. 66PCh. 28 - Prob. 67PCh. 28 - Prob. 68PCh. 28 - Prob. 69PCh. 28 - Prob. 70PCh. 28 - Prob. 71PCh. 28 - Prob. 72PCh. 28 - Prob. 73PCh. 28 - Prob. 74PCh. 28 - Prob. 75PCh. 28 - Prob. 76PCh. 28 - Prob. 77PCh. 28 - Prob. 79PCh. 28 - Prob. 78PCh. 28 - Prob. 80PCh. 28 - Prob. 81PCh. 28 - Prob. 82PCh. 28 - Prob. 83PCh. 28 - Prob. 84P
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