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: Convert the ionization energy from J/mol to J/atom. The given ionization energy is for one mole of Titanium atoms. To find the energy required to ionize a single atom, we divide by Avogadro's number (N_A). E_atom = E_molN_A E_atom = 6.36 × 10^5 J/mol6.02 × 10^23 mol^-1 E_atom = 1.056478 × 10^-18 J Step 2: Use the relationship between energy, Planck's constant, speed of light, and wavelength. The energy of a photon (E) is related to its wavelength (), Planck's constant (h), and the speed of light (c) by the formula: E = (hc)/() Step 3: Rearrange the formula to solve for the wavelength (). = (hc)/(E_atom) Step 4: Substitute the values and calculate the wavelength. h = 6.63 × 10^-34 Js c = 3.0 × 10^8 m/s E_atom = 1.056478 × 10^-18 J = (6.63 × 10^-34 Js) × (3.0 × 10^8 m/s)1.056478 × 10^-18 J = 1.989 × 10^-25 Jm1.056478 × 10^-18 J = 1.8826 × 10^-7 m Step 5: Convert the wavelength from meters to nanometers (nm). Since 1 nm = 10^-9 m: = 1.8826 × 10^-7 m × 1 nm10^-9 m = 188.26 nm Step 6: Compare the calculated wavelength with the given options. The calculated wavelength is approximately 188.3 nm. A. 0.188 nm B. 1.88 nm C. 18.8 nm D. 188.0 nm The closest option is D. The final answer is D. 188.0 nm. That's 2 down. 3 left today — send the next one.