JEE Mains · Physics · STD 11 - 12 . kinetic theory of gases
The mean free path of a molecule of diameter \(5\times10^{-10}\) m at the temperature \(41^{\circ}C\) and pressure \(1.38\times10^{5}Pa\), is given as ___________ m.
(Given \(k_{B}=1.38\times10^{-23}J/K\)).
- A \(2\sqrt{2}\times10^{-10}\)
- B \(10\sqrt{2}\times10^{-8}\)
- C \(2\sqrt{2}\times10^{-8}\)
- D \(2\times10^{-8}\)
Answer & Solution
Correct Answer
(C) \(2\sqrt{2}\times10^{-8}\)
Step-by-step Solution
Detailed explanation
\(\lambda=\frac{k_{B}T}{\sqrt{2}\pi\sigma^{2}P}\) \(=\frac{1.38\times10^{-23}\times(273+41)\times100}{\sqrt{2}\times3.14\times(5\times10^{-10})^{2}\times1.38\times10^{5}}=2\sqrt{2}\times10^{-8}\)
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Physics
- A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate \(\frac{ dM ( t )}{ dt }= bv ^{2}( t ),\) where \(v ( t )\) is its instantaneous velocity. The instantaneous acceleration of the satellite isJEE Mains 2020 Hard
- A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature \(50^{\circ} C\). The gas is now heated to double its temperature. The modified pressure is _________ Pa .JEE Mains 2026 Hard
- A potential barrier of \(0.4 \,V\) exists across a p-n junction. An electron enters the junction from the \(n\)-side with a speed of \(6.0 \times 10^{5} \,ms ^{-1}\). The speed with which electron enters the \(p\) side will be \(\frac{x}{3} \times 10^{5} \,ms ^{-1}\) the value of \(x\) is .............. (Given mass of electron \(=9 \times 10^{-31} \,kg\), charge on electron \(=1.6 \times 10^{-19} \,C\).)JEE Mains 2022 Hard
- According to Bohr's theory, the moment of momentum of an electron revolving in \(4^{\text {th }}\) orbit of hydrogen atom is _______.JEE Mains 2024 Hard
- A parallel plate capacitor filled with a medium of dielectric constant \(10\) , is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant \(15\) . Then the energy of capacitor will ......................JEE Mains 2022 Hard
- In a series \(LCR\) resonant circuit, the quality factor is measured as \(100\) If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be .........JEE Mains 2021 Hard
More PYQs from JEE Mains
- For a positive integer \(n,\left(1+\frac{1}{x}\right)^{n}\) is expanded in increasing powers of \(x\). If three consecutive coefficients in this expansion are in the ratio, \(2: 5: 12,\) then \(n\) is equal toJEE Mains 2020 Medium
- Let \(A\) be a square matrix such that \(A A^T=I\). Then \(\frac{1}{2} A\left[\left(A+A^T\right)^2+\left(A-A^T\right)^2\right]\) is equal toJEE Mains 2024 Medium
- For \(0<\theta<\pi / 2\), if the eccentricity of the hyperbola \(\mathrm{x}^2-\mathrm{y}^2 \operatorname{cosec}^2 \theta=5\) is \(\sqrt{7}\) times eccentricity of the ellipse \(x^2 \operatorname{cosec}^2 \theta+y^2=5\), then the value of \(\theta\) is :JEE Mains 2024 Medium
- The system of linear equations \(x + \lambda y - z = 0,\lambda x - y - z = 0\;,\;x + y - \lambda z = 0\) has a non-trivial solution for:JEE Mains 2016 Medium
- \(\operatorname{cosec} 18^{\circ}\) is a root of the equation :JEE Mains 2021 Hard
- The radius of a nucleus of mass number \(64\) is \(4.8\) fermi. Then the mass number of another nucleus having radius of \(4\) fermi is \(\frac{1000}{x}\), where \(x\) is _______.JEE Mains 2024 Hard