A student has plotted the graph to determine Planck's Constant and drawn two lines of extreme fit, one of maximum slope that still fits the points (m1) and one of minimum slope that still fits the points (m2). This is shown in the figure below.The student wants to determine the slope of m1. The two data point values which lie on m1 are of the form (x1,y1) and (x2,y2).Using the two points (4.5 x 1014 Hz, 0.18 V) and (7.9 x 1014Hz, 1.18 V); determine the value of the gradient to three significant figures. Use SI units.Entering numbers in scientific notation: Example: 1.45 x 10-9 should be entered as 1.45E-9
Question
A student has plotted the graph to determine Planck's Constant and drawn two lines of extreme fit, one of maximum slope that still fits the points (m1) and one of minimum slope that still fits the points (m2). This is shown in the figure below.The student wants to determine the slope of m1. The two data point values which lie on m1 are of the form (x1,y1) and (x2,y2).Using the two points (4.5 x 1014 Hz, 0.18 V) and (7.9 x 1014Hz, 1.18 V); determine the value of the gradient to three significant figures. Use SI units.Entering numbers in scientific notation: Example: 1.45 x 10-9 should be entered as 1.45E-9
Solution
The gradient or slope of a line is determined by the change in the y-values divided by the change in the x-values. In this case, the y-values are voltage (V) and the x-values are frequency (Hz).
The formula for the slope (m) is:
m = (y2 - y1) / (x2 - x1)
Substituting the given values into the formula:
m = (1.18 V - 0.18 V) / ((7.9 x 10^14 Hz) - (4.5 x 10^14 Hz)) m = 1 V / 3.4 x 10^14 Hz m = 2.94 x 10^-15 V/Hz
So, the slope of the line m1 is approximately 2.94 x 10^-15 V/Hz to three significant figures.
Similar Questions
A student has plotted the graph and drawn two lines of extreme fit, one of maximum slope that still fits the points (m1) and one of minimum slope that still fits the points (m2). This is shown in the figure below.The student wants to determine the slope of m1. The two data point values which lie on m1 are of the form (x1,y1) and (x2,y2).Using the two points (0.04 m2, 0.15 N) and (0.43 m2, 1.12 N); determine the value of the gradient to two decimal places including units.
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