Step 1: Understand the question.
We must find how the magnetic moment $M$ of an electron in a Bohr orbit depends on the principal quantum number $n$.
Step 2: Link magnetic moment to angular momentum.
For a revolving electron, the magnetic moment is tied to the orbital angular momentum $L$ through the gyromagnetic ratio:
\[ M = \frac{e}{2m_e}\,L \]
Step 3: Use Bohr's quantization.
Bohr's rule says the angular momentum is quantized:
\[ L = \frac{nh}{2\pi} \]
Step 4: Put $L$ into the moment formula.
\[ M = \frac{e}{2m_e}\times \frac{nh}{2\pi} = \frac{eh}{4\pi m_e}\,n \]
Step 5: Spot the constant.
The group $\dfrac{eh}{4\pi m_e}$ is made only of fixed constants (it is the Bohr magneton). So it does not change with the orbit.
Step 6: Read off the proportionality.
Since the constant part is fixed, the magnetic moment grows in direct step with $n$:
\[ M \propto n \]
This matches option (2).
\[ \boxed{M \propto n} \]