The correct answer is A. n2.
The number of waves in an orbit is given by the de Broglie equation, $n\lambda = 2\pi r$, where $n$ is the principal quantum number, $\lambda$ is the wavelength of the electron, and $r$ is the radius of the orbit. The radius of the nth Bohr orbit is given by $r_n = n^2 a_0$, where $a_0$ is the Bohr radius. Substituting this into the de Broglie equation, we get $n\lambda = 2\pi n^2 a_0$, or $\lambda = \frac{2\pi n a_0}{n}$. Therefore, the number of waves in the nth Bohr orbit is $n^2$.
Option B is incorrect because it does not take into account the radius of the orbit. Option C is incorrect because it does not take into account the de Broglie wavelength of the electron. Option D is incorrect because it does not take into account the principal quantum number.