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Dual Nature of Radiation and Matter question

2017 · Q139
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Dual Nature of Radiation and Matter question

2017 · Q139

NEETPhysicsDual Nature of Radiation and MatterMCQ+4 / −1
The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature T (kelvin) and mass m, is
  1. A
    h3mkT{h \over {\sqrt {3mkT} }}3mkT​h​
  2. B
    2h3mkT{{2h} \over {\sqrt 3 mkT}}3​mkT2h​
  3. C
    2hmkT{{2h} \over {\sqrt {mkT} }}mkT​2h​
  4. D
    hmkT{h \over {\sqrt {mkT} }}mkT​h​
View written solutionFree

Correct answer: A

Wavelength, λ\lambda λ = hp{h \over p}ph​

⇒\Rightarrow⇒ λ\lambda λ = h2mE{h \over {\sqrt {2mE} }}2mE​h​

⇒\Rightarrow⇒ λ\lambda λ = h2m×32kT{h \over {\sqrt {2m \times {3 \over 2}kT} }}2m×23​kT​h​

⇒\Rightarrow⇒ λ\lambda λ = h3mkT{h \over {\sqrt {3mkT} }}3mkT​h​

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