Question

A negatively charged particle called Negatron was discovered. In the Millikan's oil-drop experiment, the charges of the oil-drops in five experiments are reported as $3.2\times {10}^{-19}$ coulomb; $4.8\times {10}^{-19}$ coulomb; $6.4\times {10}^{-19}$ coulomb; $8\times {10}^{-19}$ coulomb and $9.6\times {10}^{-19}$ coulomb. Calculate the charge on the negatron.

Answer 1

In Millikan's oil-drop experiment; the charges on the oil-drops are integral multiples of the charge of the particles.
Dividing the charges of droplets by the lowest charge:
(i) $\frac{3.2\times {10}^{-19}}{3.2\times {10}^{-19}}=1$
(ii) $\frac{4.8\times {10}^{-19}}{3.2\times {10}^{-19}}=1.5$
(iii) $\frac{6.4\times {10}^{-19}}{3.2\times {10}^{-19}}=2$
(iv) $\frac{8\times {10}^{-19}}{3.2\times {10}^{-19}}=2.5$
(v) $\frac{9.6\times {10}^{-19}}{3.2\times {10}^{-19}}=3$
All the values are not integral; they can be converted to integers on multiplying by $2$.
$\therefore$ Charge of the negatron will be
$\frac{3.2\times {10}^{-19}}{2}=1.6\times {10}^{-19}C$.