The carbon isotope ¹⁴C is used for carbon dating of archeological artifacts. ¹⁴C (mass 2.34 × 10^-26 kg) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, the electron and the neutrino are emitted at right angles to each other. The electron (mass 9.11 × 10^-31 kg) has a speed of 5.0 × 10⁷ m/s and the neutrino has a momentum of 8.0 × 10-²⁴ kg m/s. What is the recoil speed of the nucleus?