The de-Broglie wavelength of a neutron in thermal equilibrium with heavy water at a temperature $T$ (Kelvin) and mass $m$, is :
- $\frac{h}{\sqrt{3m kT}}$
- $\frac{2h}{\sqrt{3m kT}}$
- $\frac{2h}{\sqrt{m kT}}$
- $\frac{h}{\sqrt{m kT}}$
The Correct Option is A
Solution and Explanation
$\lambda =\frac{h}{m v}$
$=\frac{h}{\sqrt{2 m( KE )}}$
$=\frac{h}{\sqrt{2 m\left(\frac{3}{2} k T\right)}}$
$\lambda =\frac{h}{\sqrt{3 m k T}}$
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Concepts Used:
Dual Nature of Radiation and Matter
The dual nature of matter and the dual nature of radiation were throughgoing concepts of physics. At the beginning of the 20th century, scientists untangled one of the best-kept secrets of nature – the wave-particle duplexity or the dual nature of matter and radiation.
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The photoelectric effect is a phenomenon that involves electrons getting away from the surface of materials.
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Heisenberg’s Uncertainty Principle states that both the momentum and position of a particle cannot be determined simultaneously.