The electrons in a beam are moving at 18 m/s. (melectron = 9.11 * 10^-31 kg, h = 6.626 * 10^-34 J ∙ s) (a) What is its momentum?

(b) What is its de Broglie wavelength these electrons?

(c) If the electron beam falls normally on a diffraction grating, what would have to be the spacing between slits in the grating to give a first-order maximum at an angle of 30° with the normal to the grating?

Question

Physics

Sincere White

24 October, 05:12

The electrons in a beam are moving at 18 m/s. (melectron = 9.11 * 10^-31 kg, h = 6.626 * 10^-34 J ∙ s) (a) What is its momentum?

(b) What is its de Broglie wavelength these electrons?

(c) If the electron beam falls normally on a diffraction grating, what would have to be the spacing between slits in the grating to give a first-order maximum at an angle of 30° with the normal to the grating?

+3

Answers (1)

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Anne Harris · Answer 1

a) momentum = m x v

= 9.11 x 10⁻³¹ x 18

= 163 x 10⁻³¹ kg m / s

b) de Broglie wavelength (λ)

= h / mv

= 6.626 x 10⁻³⁴ / 163 x 10⁻³¹

= 40.65 x 10⁻⁶ m.

λ = 40.65 x 10⁻⁶ m

c) angle of first order maxima

= λ / a where a is the spacing between slits

sin 30 = λ / a

a = 40.65 x 10⁻⁶ /.5

= 81.3 x 10⁻⁶ m

=.0813 mm.