Name: De Broglie's Explanation of Bohr's Second Postulate
Uploaded: 2019-07-19
Duration: 1 min 30 s
Description: How does one explain Bohr's second postulate of quantisation of orbital angular momentum using de Broglie's hypothesis? Watch this video and find out.

Question

Explain the distance of closest approach and impact parameter.

Accepted Answer

Let an alpha particle with an initial kinetic energy $E$ be directed towards the nucleus of an atom. Now, since both alpha particle and nucleus exhibits positive charge, there would be a repulsive force between them. This Coulomb's repulsive force between the nucleus and the alpha particle would increase as the alpha particle closes in on the nucleus and as a result the kinetic energy of the alpha particle would keep on decreasing. At a certain distance $r_{0}$ , the kinetic energy of the alpha particle reduces to zero, and it retraces its path back to $180 °$ . This distance $r_{0}$ is called the distance of closest approach.

$r_{0} = \frac{(Z e) (2 e)}{4 π ε_{0} (\frac{1}{2} m v^{2})}$ where $Z$ is the atomic number of the nucleus, $m$ is the mass of the alpha particle and $v$ is its initial velocity.

Impact parameter is defined as the perpendicular distance of the initial velocity vector of the alpha particle from the central line of the nucleus when the particle is far away from the nucleus.

$b = \frac{1}{4 π ε_{0}} \frac{Z e^{2} c o t \frac{θ}{2}}{E}$ where $E$ is the kinetic energy of the alpha particle such that $E = \frac{1}{2} m v^{2}$ and $θ$ is the scattering angle.

Explain the distance of closest approach and impact parameter.

Important Questions on Atoms

Learn and Prepare for any exam you want !