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NCERT Class XII Chapter
Dual Nature of Radiation and Matter
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Question : 14
Total: 37
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.
Solution:  
(a) Kinetic energy required by electron to have de-Broglie wavelength of 589 nm
K =
h2
2mλ2
 =
(6.63×10−34)2
2×9.1×10−31×(589×10−9)2
K = 6.95 × 10–25 J = 4.34 µeV
(b) Kinetic energy of neutron to have de-Broglie wavelength of 589 nm
K =
h2
2mλ2
 =
(6.63×10−34)2
2×1.67×10−27×(589×10−9)2
K = 3.78 × 10–28 J = 2.36 neV
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