The slope of the stopping voltage versus frequency graph was found to be m = (4.36 ± 0.75) x 10-15 Vs. Using this value to determine Planck's constant we obtain h = 6.976 x 10-34Js.Determine the uncertainty in h. Express you answer to 2 significant figures in SI units.Entering numbers in scientific notation: Example: 1.45 x 10-9 should be entered as 1.45E-9
Question
The slope of the stopping voltage versus frequency graph was found to be m = (4.36 ± 0.75) x 10-15 Vs. Using this value to determine Planck's constant we obtain h = 6.976 x 10-34Js.Determine the uncertainty in h. Express you answer to 2 significant figures in SI units.Entering numbers in scientific notation: Example: 1.45 x 10-9 should be entered as 1.45E-9
Solution
The uncertainty in a calculated quantity can be determined using the formula for the propagation of uncertainty. In this case, the uncertainty in Planck's constant (h) is determined by the uncertainty in the slope (m) of the stopping voltage versus frequency graph.
The formula for the propagation of uncertainty is:
Δh = |dh/dm| * Δm
where Δh is the uncertainty in h, dh/dm is the derivative of h with respect to m, and Δm is the uncertainty in m.
Since h is directly proportional to m (h = m), the derivative dh/dm = 1.
Therefore, the uncertainty in h is:
Δh = |1| * Δm Δh = Δm
The uncertainty in the slope m was given as 0.75 x 10^-15 Vs. Therefore, the uncertainty in Planck's constant is the same:
Δh = 0.75 x 10^-15 Js
Expressed to two significant figures in SI units, the uncertainty in Planck's constant is 7.5 x 10^-16 Js.
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