Question

Which of the following curves may represent the speed of the electron in a hydrogen atom as a function of the principal quantum number n?

Answer 1

(c)

The speed (v) of electron can be expressed as
$v=\frac{Z{e}^2}{2{\in }_{0}hn}$ ....(1)
Here,
Z = Number of protons in the nucleus
e = Magnitude of charge on electron charge
n = Principal quantum number
h = Planck's constant

It can be observed from equation (1) that the velocity of electron is inversely proportional to the principal quantum number (n).
Therefore, the graph between them must be a rectangular hyperbola.
The correct curve is (c).