JEE Mains · Physics · STD 12 - 11. Dual nature of radiation and matter
The de Broglie wavelength of an oxygen molecule at \(27^{\circ} C\) is \(x \times 10^{-12} m\). The value of \(x\) is (take Planck's constant \(=6.63 \times 10^{-34} J . s\), Boltzmann constant \(=1.38 \times 10^{-23} J / K\), mass of oxygen. Molecule \(\left.=5.31 \times 10^{-26} kg\right)\).
- A 26
- B 24
- C 30
- D 20
Answer & Solution
Correct Answer
(A) 26
Step-by-step Solution
Detailed explanation
\( \lambda=\frac{h}{\sqrt{2mK}}=\frac{h}{\sqrt{2m(\frac{3}{2}kT)}} \) \( \lambda=\frac{h}{\sqrt{3mkT}} \) \( =\frac{6.63\times10^{-34}}{\sqrt{3\times5.31\times10^{-26}\times1.38\times10^{-23}\times300}} \) \( =2.58\times10^{-11}=25.8\times10^{-12} \) So, \( x=26 \)
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