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Question: The charge on 1 microgram\(\left( {\mu g} \right)\)electron will be................ (mass of an elec...

The charge on 1 microgram(μg)\left( {\mu g} \right)electron will be................ (mass of an electron=9.11×10−31kg = 9.11 \times {10^{ - 31}}kg)
A) 176×10−3C176 \times {10^{ - 3}}C
B) 176×100C176 \times {10^0}C
C) 176×103C176 \times {10^3}C
D) 176×105176 \times {10^5}

Explanation

Solution

Electrons are charged particles. Electrons have negative charge. The mass of the electron is given in the question. The charge of an electron is 1.6×1019C1.6 \times {10^{19}}C. If the mass and charge of a single electron is known, then using that relation we can find the equivalent charge of any mass of the electron.

Complete step by step solution:
The mass of a single electron is given in the question,
Mass of an electron =9.11×10−31kg = 9.11 \times {10^{ - 31}}kg
We know that, the charge of a single electron is 1.6×1019C1.6 \times {10^{19}}C
This means that, the charge equivalent to 9.11×10−31kg9.11 \times {10^{ - 31}}kg of electron is 1.6×1019C1.6 \times {10^{19}}C
9.11×10−31kg⇒1.6×1019C9.11 \times {10^{ - 31}}kg \Rightarrow 1.6 \times {10^{19}}C
Now, from this relation
1kg⇒1.6×10−199.11×10−311kg \Rightarrow \dfrac{{1.6 \times {{10}^{ - 19}}}}{{9.11 \times {{10}^{ - 31}}}} (Divide using 9.11×10−31kg9.11 \times {10^{ - 31}}kgon both sides)
1μg=1×10−6×10−3kg⇒1.6×10−19×10−6×10−99.11×10−311\mu g = 1 \times {10^{ - 6}} \times {10^{ - 3}}kg \Rightarrow \dfrac{{1.6 \times {{10}^{ - 19}} \times {{10}^{ - 6}} \times {{10}^{ - 9}}}}{{9.11 \times {{10}^{ - 31}}}} (∵1μ=10−6,1g=10−3kg\because 1\mu = {10^{ - 6}},1g = {10^{ - 3}}kg)
Calculating the above equation we get,
1μg⇒1.69.1×103C1\mu g \Rightarrow \dfrac{{1.6}}{{9.1}} \times {10^3}C
⇒0.176×103C\Rightarrow 0.176 \times {10^3}C
⇒176×100C\Rightarrow 176 \times {10^0}C

The correct answer is: option (B) 176×100C176 \times {10^0}C

Note: The mass and charge of the electron, proton and the mass of the neutron will be required while doing problems. One should be thorough with these values. Protons are much heavier than electrons. Mass of a proton is 1.673×10−27Kg1.673 \times {10^{ - 27}}Kg. The mass of a neutron is 1.675×10−27kg1.675 \times {10^{ - 27}}kg. Protons and electrons have the same magnitude for charge while proton is positively charged and electron is negatively charged. Neutrons are neutral particles which do not possess any charge. There is no relation between charge and mass of a charged body. They are two independent aspects. Another important fact to be taken care of the order of magnitude. In questions involving values in the order of micro, nano, pico etc. we need to know how to convert it into corresponding kilograms. Kilogram is the basic unit of mass in the SI system.