This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.
ScanSolve AI Answer
Step 1: Recall the de Broglie wavelength formula. The de Broglie wavelength () of a particle is given by the formula: = (h)/(mv) where: • h is Planck's constant (6.626 × 10^-34 J s) • m is the mass of the particle • v is the velocity of the particle Step 2: Identify the given values and necessary constants. • Mass of an electron, m_e = 9.109 × 10^-31 kg • Velocity of the electron, v = 2.18 × 10^6 m/s • Planck's constant, h = 6.626 × 10^-34 J s Step 3: Substitute the values into the de Broglie wavelength formula. = 6.626 × 10^-34 J s(9.109 × 10^-31 kg) × (2.18 × 10^6 m/s) Step 4: Calculate the denominator. m × v = (9.109 × 10^-31 kg) × (2.18 × 10^6 m/s) m × v = (9.109 × 2.18) × (10^-31 × 10^6) kg m/s m × v = 19.85762 × 10^-25 kg m/s Step 5: Calculate the wavelength. = 6.626 × 10^-34 J s19.85762 × 10^-25 kg m/s = (6.626)/(19.85762) × 10^-34 - (-25) m = 0.33367 × 10^-9 m Step 6: Convert the wavelength to nanometers (nm). Since 1 nm = 10^-9 m: = 0.33367 nm Rounding to two significant figures, as suggested by the options: ≈ 0.33 nm The wavelength will be 0.33 nm. 3 done, 2 left today. You're making progress.