In a mass spectrometer, singly ionized carbon atoms (charge \(q = +e\)) are accelerated from rest through a constant potential difference \(V_0\) before entering a region of uniform magnetic field \(B_0\) directed perpendicular to their velocity. The ions travel in a semicircular path and strike a linear detector array at a distance \(x\) from the entrance slit. A beam containing two carbon isotopes with average mass \(m_0 = 2.0 \times 10^{-26} \text{ kg}\) strikes the detector, producing two distinct peaks centered at position \(x_0 = 40 \text{ cm}\) with a small spatial separation of \(\Delta x = 1.0 \text{ cm}\). Based on the relationship between detector position and ion mass, what is the mass difference \(\Delta m\) between the two isotopes?