A hypothetical subatomic particle has a charge of \(-e\) and a mass equal to \(2m_e\), where \(m_e\) is the mass of an electron. The particle is bound to a single proton to form a hydrogen-like system. Assuming the Bohr model applies to this system, how does the radius \(r'\) of the particle's ground-state orbit (\(n=1\)) compare to the ground-state Bohr radius \(r_1\) of a standard hydrogen atom?