Identify the curve from the figure below that could depict the...

The speed of an electron in the $n^{\text{th}}$ Bohr orbit of a hydrogen atom is given by:

$v_n = \dfrac{Z e^2}{2 \epsilon_0 n h}$

For a hydrogen atom, $Z = 1$, which gives:

$v_n \propto \dfrac{1}{n}$

This indicates that the speed $v$ is inversely proportional to the principal quantum number $n$. The graph of an inversely proportional relationship ($y \propto \dfrac{1}{x}$) is a rectangular hyperbola.

Analyzing the given curves:
Curve a shows an increasing trend.
Curve b shows a linear decrease.
Curve c represents a rectangular hyperbola, showing a rapid decrease that gradually flattens out, which matches $v \propto \dfrac{1}{n}$.
Curve d shows an increasing trend.

Thus, curve c correctly depicts the variation of $v$ with $n$.