The wavelength of light from the spectral emission line of sodium is 589 nm. Find the kinetic energy at which (a) an electron, and (b) a neutron, would have the same de Broglie wavelength.

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Wavelength of light of a sodium line, λ = 589 nm = 589 × 10−9 m Mass of an electron, me= 9.1 × 10−31 kg Mass of a neutron, mn= 1.66 × 10−27 kg Planck’s constant, h = 6.6 × 10−34 Js (a) For the kinetic energy K, of an electron accelerating with...
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Wavelength of light of a sodium line, λ = 589 nm = 589 × 10−9 m Mass of an electron, me= 9.1 × 10−31 kg Mass of a neutron, mn= 1.66 × 10−27 kg Planck’s constant, h = 6.6 × 10−34 Js (a) For the kinetic energy K, of an electron accelerating with a velocity v, we have the relation: We have the relation for de Broglie wavelength as: Substituting equation (2) in equation (1), we get the relation: Hence, the kinetic energy of the electron is 6.9 × 10−25 J or 4.31 μeV. (b) Using equation (3), we can write the relation for the kinetic energy of the neutron as: Hence, the kinetic energy of the neutron is 3.78 × 10−28 J or 2.36 neV. read less
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