Which of the plots shown in the figure represents speed $(v)$ of the electron in a hydrogen atom as a…
Which of the plots shown in the figure represents speed $(v)$ of the electron in a hydrogen atom as a function of the principal quantum number $(n)$ ?
$B$
$D$
$C$
$A$
Solution
Velocity of electron in $n^{\text {th }}$ orbit of hydrogen atom is given by :
$
V_n=\frac{2 \pi K Z e^2}{n h}
$
Substituting the values we get,
$
V_n=\frac{2.2 \times 10^6}{n} \mathrm{~m} / \mathrm{s} \quad \text { or } \quad V_n \propto \frac{1}{n}
$
As principal quantum number increases, velocity decreases
