In each case, identify the element in question. (a) The mass...

In each case, identify the element in question. (a) The mass number of an atom is $234,$ and the atom has $60.0 \%$ more neutrons than protons. (b) An ion with a +2 charge has $10.0 \%$ more protons than electrons. (c) An ion with a mass number of 110 and a $2+$ charge has $25.0 \%$ more neutrons than electrons.

In each case, identify the element in question.
(a) The mass number of an atom is $234,$ and the atom has $60.0 \%$ more neutrons than protons.
(b) An ion with a +2 charge has $10.0 \%$ more protons than electrons.
(c) An ion with a mass number of 110 and a $2+$ charge has $25.0 \%$ more neutrons than electrons.

Key Concepts

Mass Number

The mass number is the sum of the number of protons and neutrons in an atom’s nucleus. It reflects the overall mass of the nucleus and is used to describe different isotopes of the same element, which vary only in their neutron count.

Ions and Charge

Ions are atoms or molecules that have gained or lost electrons, resulting in a net electrical charge. The charge state of an ion, indicated by symbols like 2+ or 2-, reflects the imbalance between the number of protons and electrons, and it plays a crucial role in determining the ion’s chemical behavior.

Atomic Number

The atomic number represents the number of protons in an atom’s nucleus. It is the fundamental identifier of an element, as each element has a unique number of protons, irrespective of the number of neutrons or electrons present.

Transcript

00:01 This problem is really, really great because it truly teaches us the important concepts of atomic theory, which is determining the number of protons, neutrons, and electrons.

00:12 And more importantly, this teaches us how to do this with ions and not knowing the element.

00:17 That's what we need to figure out.

00:19 So this problem is really interesting.

00:22 For part a, we're going to say let p be the number of protons.

00:26 And based on the information we're given about our unknown element.

00:31 Our neutrons will be equivalent to 0 .6p plus p.

00:36 Now remember that if we want to find the number of mass in an element, mass is equivalent to the number of protons plus the number of neutrons.

00:46 So for this element, we'll have 234 as equivalent to p multiplied by 1 plus 0 .6 plus 1.

00:56 This is just substituting the equations for neutrons into our equations for mass.

01:01 And we'll find that 234 is equivalent to p multiplied by 2 .6.

01:08 So if we want to know p because remember the number of protons indicates which element is which on the periodic table, we'll have 234 divided by 2 .6 and we'll get 90.

01:22 So from here we can determine that our unknown element in part a is thorium.

01:29 Now on to part b, this is a very similar procedure, but now we're dealing with an ion.

01:35 So we have to talk about the number of electrons.

01:38 We're going to say let e be the number of electrons that we have, and our number of protons, based on the information we're given, will be equivalent to e plus 0 .1e, and now the number of electrons will be equal to protons minus 2.

01:54 And we'll use the substitution later on.

01:58 So we'll have 1 .1e minus e is equivalent to 2.

02:02 Is just basically combining the equations we've had so far, and we'll have 0 .1e as equivalent to 2...

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