Question

Is the velocity of an electron in all orbits the same for an atom of a particular element? How does it vary for different single electron species? Give reasons in support of your answer.

Answer 1

1. No, an atom of a specific element does not have the same electron velocity in all orbits.
2. From the forces acting on moving electron relationship,
   $\mathrm{mvr}=\frac{nh}{2\pi }$
   where, $n$ is the number of orbit, $m$ is the mass of electron, $v$ is the velocity of the electron, $r$ is the radius of the orbit, $h$ is Planck's constant.
   $\therefore \mathrm{v}=\frac{nh}{2\pi mr}$
3. This relationship represents that velocity is directly proportional to the number of orbits, provided the other values in the expression are constant. Thus, the velocity of an electron is not the same in all orbits for an atom of a particular element.
4. The velocity of an electron can be related with the atomic number as:
   $v_n\propto \frac{Z}{n}$
5. Here, $\mathrm{Z}$ is the atomic number and $\mathrm{n}$ is the number of orbits. Thus, the velocity increases with an increase in atomic number and decreases with an increase in a number of orbits.
6. For different single electron species, the value of $n$ is 1 . However, as the atomic number increases, the velocity of the electron will increase.

Hence, The velocity of an electron in all orbits is not the same for an atom of a particular element.