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JEE Mains · Physics · STD 12 - Dual nature of radiation and matter
- JEE Mains 2021
- Medium
- MCQ
The temperature of an ideal gas in \(3-\)dimensions is \(300\, {K}\). The corresponding de-Broglie wavelength of the electron approximately at \(300\,{K}\), is \(....\,nm\) \(\left\lfloor{m}_{e}=\text { mass of electron }=9 \times 10^{-31} \,{kg}\right.\) \({h}=\text { Planck constant }=6.6 \times 10^{-34} {Js}\) \(\left.{k}_{{B}}=\text { Boltzmann constant }=1.38 \times 10^{-23}\, {JK}^{-1}\right]\)
Pick an option to check your answer.
Answer & Solution
Correct Answer
(A) \(6.26\)
Step-by-step Solution
Detailed explanation
De-Broglie wavelength
\(\lambda=\frac{{h}}{{mv}}=\frac{{h}}{\sqrt{2 {mE}}}\)
Where \({E}\) is kinetic energy
\({E}=\frac{3 {kT}}{2} \text { for gas }\)
\(\lambda=\frac{{h}}{\sqrt{3 {mkT}}}=\frac{6.6 \times 10^{-34}}{\sqrt{3 \times 9 \times 10^{-31} \times 1.38 \times 10^{-23} \times 300}}\)
\(\lambda=6.26 \times 10^{-9}\, {m}=6.26\, {nm}\)
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