Electrons moving in a beam have the same de Broglie wavelength as protons in a separate beam moving at a speed of 2.8 × 10^4 m/s . What is the speed of the electrons?

de Broglie wavelength formula:
λ = h/mv,
whereλ = wavelength,h = Planck's Constant = 6.626 x 10^-34 Js,m = mass of object,v = object's velocity,
Mass of proton m_p = 1.6726219 × 10^-27 kg,Velocity of proton v_p = 2.8 × 10⁴ ms^-1 ,Mass of electron m_e = 9.11 × 10^-31 kg,
de Broglie wavelength of proton λ_p= h/m_pv_p = (6.626x10^-34)/[(1.6726219 × 10^-27)(2.8 × 10⁴)] = 1.4170 x 10^-11 m,de Broglie wavelength of electron λ_e= h/m_ev_e = λ_p= 1.4170 x 10^-11 m,
Rearranging for v_e, we get,
v_e= h/λ_em_e, v_e = (6.626x10^-34)/[(1.4170 x 10^-11)(9.11 × 10^-31)],v_e = 5.1328 x 10⁷ ms^-1,v_e = 5.1 x 10⁷ ms^-1 (correct to 2 significant figures)