A chemist in an imaginary universe where electrons have a different charge than they do in our universe preforms Millikan's oil drop experiment to measure the electron charge. The charges of the drops are recorded below. What is the charge of the electron in this imaginary universe?a. Drop A-6.9 X 10^-19 Cb. Drop B-9.2 X 10^-19 Cc. Drop C-11.5 X 10^-19 Cd. Drop D-4.6 X 10^-19 C

In Millikan experiment, it was discovered that the electric charge on the oil drops is discrete - and its value is always an integer multiple of a certain charge [tex]e[/tex], called fundamental charge (the charge of the electron). This is because an oil drop always contains an integer number of electrons, so the charge must be a multiple of [tex]e[/tex].

This means that we can write the charge on an oil drop as

[tex]Q=Ne[/tex]

For the drop recorded in this experiment, we have:

[tex]Q_A = N_A e = -6.9\cdot 10^{-19}C[/tex]

[tex]Q_B = N_B e = -9.2\cdot 10^{-19}C[/tex]

[tex]Q_C = N_C e = -11.5\cdot 10^{-19}C[/tex]

[tex]Q_D = N_D e = -4.6\cdot 10^{-19}C[/tex]

By dividing drop A by drop D, we get

[tex]\frac{Q_A}{Q_D}=\frac{3}{2}[/tex]

Also by dividing deop B by drop D we get

[tex]\frac{Q_B}{Q_D}=\frac{4}{2}[/tex]

And also, by dividing drop C by drop D we get

[tex]\frac{Q_C}{Q_D}=\frac{5}{2}[/tex]

This means that the charges on drop A, B, C and D are in the ratio

3 : 4 : 5 : 2

And therefore, the fundamental charge must be half of the charge on drop D:

[tex]e=\frac{Q_D}{2}=-2.3\cdot 10^{-19}C[/tex]

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