An atom of $^{14}N$ gains 3 electrons - AQA - A-Level Physics - Question 8 - 2017 - Paper 1
Question 8
An atom of $^{14}N$ gains 3 electrons.
What is the specific charge of the ion?
Worked Solution & Example Answer:An atom of $^{14}N$ gains 3 electrons - AQA - A-Level Physics - Question 8 - 2017 - Paper 1
Step 1
Calculate the charge of the ion
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Answer
The nitrogen atom (14N) has 7 protons and when it gains 3 electrons, it has an overall charge of -3e where e is the elementary charge, approximately equal to 1.60×10−19 C. Therefore, the total charge is
−3e=−3×(1.60×10−19 C)=−4.80×10−19 C.
Step 2
Determine the mass of the ion
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Answer
The mass of a nitrogen ion can be found using its atomic mass. The atomic mass of nitrogen is approximately 14 u (atomic mass units), which can be converted to kg using the conversion factor:
1extu≈1.66×10−27 kg.
Thus,
14 u≈14×(1.66×10−27extkg)≈2.32×10−26 kg.
Step 3
Calculate the specific charge
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Answer
The specific charge is defined as the charge per unit mass. Therefore, using the total charge and mass calculated:
Specific Charge=MassTotal Charge=2.32×10−26 kg−4.80×10−19 C≈−2.07×107 C kg−1.
Rounded to two significant figures, this is approximately
−1.80×107 C kg−1.
Comparing with the options provided, the correct answer is B. -1.80 × 10³ C kg⁻¹.
