Question
Question: The electrostatic force of repulsion between two equal positively charged ions is \( 3.7 \times {10^...
The electrostatic force of repulsion between two equal positively charged ions is 3.7×10−9N , when they are separated by a distance of 5A˙ . What is the number of electrons which are missing from each ion?
Solution
Hint
Convert the separation of two charged ions to metre. Then, use the Coulomb’s Law which is expressed by-
F=4πε01r2q1q2
where, q1 is the charge of first charged ions and q2 is the second charged ion
r is the separation between charged ions
It is given that charge of ions is equal
Find the charge and then calculate number of electrons by using formula- q=ne
where, n is the number of electrons and e is the charge of an electron.
Complete step by step answer
Let the force of repulsion between two charged ions be F , separation between them be r and charge on the first and second ions be q1 and q2 respectively.
According to the question, it is given that
F=3.7×10−9N
r=5A˙=5×10−10m
The charge on both the ions is equal to each other then,
q1=q2=q
Using the expression of Coulomb’s Law which can be expressed as-
F=4πε01r2q1q2
Now, putting the values given in question in their respective places
3.7×10−9=9×109×(5×10−10)2q1q2
∵q1=q2=q
∴q2=9×1091×3.7×10−9×(5×10−10)2q2=9×10992.5×10−29
Doing further calculations, we get
q2=10.28×10−38q=3.2×10−19C
Now, we got the value of charge for two charged ions
To calculate the number of electrons missing from each ion let n be the number of electrons missing and e be the charge of electrons. Use the expression-
q=ne
Putting values in their respective places
3.2×10−19=n×1.6×10−19n=1.6×10−193.2×10−19∴n=2
The number of missing electrons from each ion is 2.
Note
Coulomb’s Law states that force between two charged particles is directly proportional to product of their charges and is inversely proportional to separation between them. Its S.I unit is N(Newton).