Using the information in Table 1.1 , answer the following...

Using the information in Table 1.1 , answer the following questions. In an ion with an unknown charge, the total mass of all the electrons was determined to be $2.55 \times 10^{-26} \mathrm{g},$ while the total mass of its protons was $5.34 \times 10^{-23} \mathrm{g}$. What is the identity and charge of this ion? What are the symbol and mass number of a neutral atom whose total mass of its electrons is $3.92 \times 10^{-26} \mathrm{g}$ while its neutrons have a mass of $9.35 \times 10^{-23} \mathrm{g} ?$

Key Concepts

Atomic Structure

Atomic structure refers to the arrangement of subatomic particles within an atom, including protons, neutrons, and electrons. Protons and neutrons reside in the nucleus while electrons orbit the nucleus. Understanding atomic structure is essential because it determines the properties of an element, such as its atomic number, mass number, and chemical behavior.

Mass-to-Particle Conversion

This concept involves using the known masses of subatomic particles (protons, neutrons, and electrons) to calculate the number of each particle present in a sample. By dividing the total mass by the mass of an individual particle, one can determine the particle count, which is crucial for identifying the atomic and isotopic composition of an element or ion.

Ions and Ionic Charge

An ion is an atom or molecule that has lost or gained electrons, resulting in a net electrical charge. The ionic charge is determined by the difference between the number of protons (which are positively charged) and electrons (which are negatively charged). A balance between these numbers creates a neutral atom, while any imbalance leads to a positively or negatively charged ion.

Isotopes and Mass Number

An isotope is a variant of an element that has the same number of protons but a different number of neutrons. The mass number of an atom is the sum of its protons and neutrons. Identifying isotopes involves determining their mass number based on the counts of these subatomic particles, which is important for understanding the element's identity and properties.

Transcript

00:01 We are asked to use the information in the table that i've written right here to find the following information.

00:07 We are given an ion that has an unknown charge and we're told that the total mass of all the electrons, i'm going to abbreviate electrons, e minus, plus, and n neutral.

00:29 Electron mass total is equal to 5 .34 times 10 to the minus 23rd grams.

00:48 And the proton mass, i wrote the wrong one down here, my bad.

00:57 My electron mass is 2 .55 times 10 to the minus 26th grams.

01:06 And my proton mass total is equal to 5 .34 times 10 to the minus 23rd grams.

01:20 We're going to divide each of these by the mass per, by these masses right here.

01:32 I'm going to just convert these.

01:34 So 9 .19 times 10 to the minus 31st kilograms.

01:46 And then i'm going to go 1 ,000 grams per kilogram.

01:51 And this will equal, let me do my math.

01:57 Clear, clear.

01:57 2 .55 times 10 to the minus 26th divided by 9 .19 times 10 to the minus 31st.

02:08 Oops, see i got, got to clear the heck out of this.

02:10 2 .55 times 10 to the minus 26th divided by 1, 9 .1, 0 .19 times 10, 9 .109 times 10 to the minus 31st divided by 1 ,000 is 28 electrons.

02:39 Now let's figure out how many protons we have.

02:44 And we'll divide this by 1 .673 times 10 to the minus 27th kilograms times 1 kilogram per 1 ,000 grams.

03:01 5 .34 times 10 to the minus 23rd divided by 1 .673.

03:11 Is that right? 1 .673 times 10 to the minus 27th divided by 1 ,000 is 32 protons.

03:26 5 .34 times 10 to the minus 23rd divided by 1 .673 times 10 to the minus 23rd.

03:30 I just want to make sure i've got the right number.

03:37 1 .673.

03:45 What the heck happened to my, there we go.

03:54 So this will be, let me get to a p table here...

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