Question

{"given":"Potential difference $V = 5$ kV, current $i = 3.2$ mA $= 3.2 \\times 10^{-3}$ A, charge of electron $e = 1.6 \\times 10^{-19}$ C, time $t = 1$ s.","key_observation":"Electric current is defined as the charge flowing per unit time: $i = \\frac{ne}{t}$, where $n$ is the number of electrons passing per second. Rearranging gives $n = \\frac{it}{e}$.","option_analysis":[{"label":"(A)","text":"$2 \\times 10^{16}$","verdict":"correct","explanation":"Using $n = \\frac{it}{e} = \\frac{3.2 \\times 10^{-3} \\times 1}{1.6 \\times 10^{-19}} = 2 \\times 10^{16}$, which matches this option."},{"label":"(B)","text":"$5 \\times 10^{6}$","verdict":"incorrect","explanation":"This value is far too small; it does not result from a valid application of $n = it/e$ with the given values."},{"label":"(C)","text":"$1 \\times 10^{17}$","verdict":"incorrect","explanation":"This would require a current of 16 mA, not 3.2 mA; likely a computational error by a factor of 5."},{"label":"(D)","text":"$4 \\times 10^{15}$","verdict":"incorrect","explanation":"This is smaller than the correct answer by a factor of 5, indicating an error in substitution or arithmetic."}],"answer":"(A)","formula_steps":[]}