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 work function from electron volts (eV) to Joules (J). The work function is given as 1.82 \, eV. We use the conversion factor 1 \, eV = 1.602 × 10^-19 \, J. = 1.82 \, eV × (1.602 × 10^-19 (J)/(eV)) = 2.91564 × 10^-19 \, J Step 2: Use the formula for threshold wavelength. The relationship between work function (), Planck's constant (h), speed of light (c), and threshold wavelength (_0) is given by: = (hc)/(_0) Rearranging to solve for _0: _0 = (hc)/() Given values: h = 6.63 × 10^-34 \, Js c = 3.0 × 10^8 \, ms^-1 = 2.91564 × 10^-19 \, J Step 3: Substitute the values and calculate the threshold wavelength in meters. _0 = (6.63 × 10^-34 \, Js) × (3.0 × 10^8 \, ms^-1)2.91564 × 10^-19 \, J _0 = 19.89 × 10^-26 \, Jm2.91564 × 10^-19 \, J _0 = 6.8212 × 10^-7 \, m Step 4: Convert the wavelength from meters to nanometers (nm). Since 1 \, nm = 10^-9 \, m: _0 = 6.8212 × 10^-7 \, m × (1 \, nm)/(10^-9) \, m = 682.12 \, nm Rounding to the nearest whole number, _0 ≈ 682 \, nm. Comparing this to the given options: A. 682 nm B. 783 nm C. 880 nm D. 982 nm The calculated threshold wavelength matches option A. The final answer is A. 682 nm. Send me the next one 📸