Question 39 of 62beginner🔧 ApplyNumerical2 marks

In Milikan’s experiment, static electric charge on the oil drops has been obtained by shining X-rays. If the static electric charge on the oil drop is –1.282×101.282 \times 10⁻¹⁸ C, calculate the number of electrons present on it.

Correct Answer

In Millikan's oil drop experiment, the magnitude of the electrical charge (qq) on the droplets is always an integral multiple of the elementary electrical charge (ee). This relationship is expressed by the formula q=neq = ne, where nn represents the number of electrons.

To find the number of electrons on the oil drop, we use the given static electric charge and the accepted value of electrical charge on an electron. The total charge on the drop is −1.282×10−18 C-1.282 \times 10^{-18} \text{ C}, and the charge of a single electron is −1.602×10−19 C-1.602 \times 10^{-19} \text{ C}.

By dividing the total charge by the charge of one electron, we get n=−1.282×10−18−1.602×10−19=8n = \frac{-1.282 \times 10^{-18}}{-1.602 \times 10^{-19}} = 8. Therefore, there are 8 electrons present on the oil drop.

Exercise: EXERCISES | Q: 2.39 | (Page 41)
For More Understanding

Explanation

According to Millikan's experiment, the total charge on an oil drop is quantized and is given by q=neq = ne, where nn is an integer representing the number of electrons and ee is the charge of a single electron. By substituting the given total charge and the standard value of the electron's charge, we can solve for nn.

Solution Steps

  1. Step 1: Write down the given values. Total charge on the oil drop, q=−1.282×10−18 Cq = -1.282 \times 10^{-18} \text{ C} Charge on one electron, e=−1.602×10−19 Ce = -1.602 \times 10^{-19} \text{ C}

  2. Step 2: State the formula relating total charge to the number of electrons. From Millikan's experiment, the magnitude of electrical charge is q=neq = ne, where nn is the number of electrons.

  3. Step 3: Substitute the values into the formula to calculate nn.

    n=qen = \frac{q}{e} n=−1.282×10−18 C−1.602×10−19 Cn = \frac{-1.282 \times 10^{-18} \text{ C}}{-1.602 \times 10^{-19} \text{ C}} n=8.00n = 8.00

  4. Step 4: State the final answer. The number of electrons present on the oil drop is 8.

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