The Maxwell-Boltzmann distribution f(vx) of one-dimensional velocities vx at temperature T is [Given: A is a… · ABC26PH0731
Subject: Physical Chemistry · Chapter: Gaseous State · Topic: Gaseous State – General · Exam: JAM 2001-2022 · Marks: 2 · Difficulty: Medium
The Maxwell-Boltzmann distribution $f(v_x)$ of one-dimensional velocities $v_x$ at temperature T is [Given: A is a normalization constant such that $\int_{-\infty}^{\infty} f(v_x)\,dv_x = 1$ and $k_B$ is the Boltzmann constant]
(a)$A\exp(-mv_x^2/2k_BT)$
(b)$A\exp(-mv_x^2/k_BT)$
(c)$Av_x^2\exp(-mv_x^2/2k_BT)$
(d)$Av_x^2\exp(-mv_x^2/k_BT)$
Answer
Answer: A ✓ checked by 4AB · confidence medium
The source book printed no answer; this one was worked out and checked — see the explanation.
Explanation
The one-dimensional Maxwell distribution is Gaussian: f(v_x) = A exp(−m v_x²/2k_BT), with no v_x prefactor (that appears only in the speed distribution).