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JEE MAIN 2021
01-09-21 S2
Question
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: $\left[\mathrm{m}_{\mathrm{e}}=\right.$ mass of electron $=9 \times 10^{-31} \mathrm{~kg}$ $\mathrm{h}=$ Planck constant $=6.6 \times 10^{-34} \mathrm{Js}$ $\mathrm{k}_{\mathrm{B}}=$ Boltzmann constant $\left.=1.38 \times 10^{-23} \mathrm{JK}^{-1}\right]$
Select the correct option:
A
6.26 nm
B
8.46 nm
C
2.26 nm
D
3.25 nm
✓ Correct! Well done.
✗ Incorrect. Try again or view the solution.
Solution
De-Broglie wavelength $$ \lambda=\frac{\eta}{m v}=\frac{h}{\sqrt{2 m E}} $$ Where E is kinetic energy $$ \begin{aligned} & E=\frac{3 \mathrm{kT}}{2} \text { for gas } \\ & \lambda=\frac{\mathrm{h}}{\sqrt{3 \mathrm{mkT}}}=\frac{6.6 \times 10^{-34}}{\sqrt{3 \times 9 \times 10^{-31} \times 1.38 \times 10^{-23} \times 300}} \\ & \lambda=6.26 \times 10^{-9} \mathrm{~m}=6.26 \mathrm{~nm} \end{aligned} $$ Option (1)
Question Tags
JEE Main
Physics
Medium
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