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Chapter 30: Problem 1

How many protons and how many neutrons are there in a nucleus of (a) neon, \(\frac{21}{10} \mathrm{Ne} ;\) (b) zinc, \({ }_{30}^{65} \mathrm{Zn} ;\) (c) silver, \({ }_{47}^{108} \mathrm{Ag}\).

Short Answer

Expert verified
Neon: 10 protons, 11 neutrons; Zinc: 30 protons, 35 neutrons; Silver: 47 protons, 61 neutrons.

Step by step solution

01

Understanding Notation

In the notation \( \frac{A}{Z} X \) or \( {}_Z^A X \), \( A \) is the mass number (total number of protons and neutrons) and \( Z \) is the atomic number (number of protons). \( X \) is the element symbol.
02

Calculate for Neon

For \( \frac{21}{10} \mathrm{Ne} \), \( Z = 10 \) (protons) and \( A = 21 \) (mass number). The number of neutrons is given by \( A - Z = 21 - 10 = 11 \). So there are 10 protons and 11 neutrons.
03

Calculate for Zinc

For \( {}_{30}^{65} \mathrm{Zn} \), \( Z = 30 \) (protons) and \( A = 65 \) (mass number). The number of neutrons is \( A - Z = 65 - 30 = 35 \). Thus, there are 30 protons and 35 neutrons.
04

Calculate for Silver

For \( {}_{47}^{108} \mathrm{Ag} \), \( Z = 47 \) (protons) and \( A = 108 \) (mass number). The number of neutrons is \( A - Z = 108 - 47 = 61 \). Therefore, there are 47 protons and 61 neutrons.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Atomic Number
The atomic number is a fundamental property in chemistry. It is denoted by the symbol \( Z \) and represents the number of protons in the nucleus of an atom. This is essential because it defines the identity of an element. For every element, the atomic number is unique.
Take the element Neon, for example. In its notation \( \frac{21}{10} \mathrm{Ne} \), the '10' is its atomic number. That means every atom of Neon has 10 protons in its nucleus.
  • The atomic number \( Z \) is crucial to determine the element's position in the periodic table. For instance, Neon, with an atomic number of 10, resides in group 18.
  • Changing the atomic number alters the element completely. This is because it changes the number of protons, affecting the overall identity of the element.
Understanding the atomic number is key to unraveling the mysteries of the periodic table and elemental composition.
Mass Number
The mass number provides another critical piece of information about an atom. Represented by \( A \), it indicates the total count of protons and neutrons present in an atom's nucleus.
For example, examining Silver with the notation \( {}_{47}^{108} \mathrm{Ag} \), the '108' is the mass number.
  • It鈥檚 important to note that the mass number is not the same as the atomic mass, which accounts for isotopic distribution and atomic weighting.
  • The mass number helps in calculating the neutrons present in the atom, by the formula \( \text{neutrons} = A - Z \).
This number is immensely helpful in distinguishing between isotopes of a given element. Isotopes have the same number of protons but different numbers of neutrons, thus different mass numbers.
Neutron Calculation
The number of neutrons in an atom's nucleus is determined using a simple subtraction of the atomic number from the mass number. This is because the mass number \( A \) consists of both protons and neutrons.
Consider the atom of zinc \( {}_{30}^{65} \mathrm{Zn} \). Given that the mass number \( A = 65 \) and the atomic number \( Z = 30 \), the formula for calculating neutrons is:
\[ \text{Neutrons} = A - Z = 65 - 30 = 35 \]
  • Neutrons play a significant role in the stability of an atom.
  • They act as a buffer between the protons, which repel each other due to their positive charge.
Knowing how to find the number of neutrons helps in understanding atomic stability and isotopic variations.
Proton Count
Protons are positively charged particles located within an atom's nucleus. Their count within the nucleus is denoted by the atomic number \( Z \). The proton count is fundamental because it directly corresponds to an element's identity.
In our exercise, Neon has a proton count of 10 as given by \( \frac{21}{10} \mathrm{Ne} \). Similarly, Zinc and Silver have proton counts of 30 and 47, respectively.
  • The number of protons defines what element the atom represents, hence why protons are so critical in chemistry.
  • Changes in the number of protons lead to a different element altogether, unlike changes in electron numbers which create ions.
Understanding the proton count is essential for identifying elements and exploring the foundational blocks of matter. It paints the atomic landscape by anchoring each unique element on the periodic table.

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Most popular questions from this chapter

An unstable isotope of cobalt, \({ }^{60} \mathrm{Co}\), has one more neutron in its nucleus than the stable \({ }^{59} \mathrm{Co}\) and is a beta emitter with a half-life of 5.3 years. This isotope is widely used in medicine. A certain radiation source in a hospital contains \(0.0400 \mathrm{~g}\) of \({ }^{60} \mathrm{Co}\). (a) What is the decay constant for that isotope? (b) How many atoms are in the source? (c) How many decays occur per second? (d) What is the activity of the source, in curies?

I A radioisotope has a half-life of 5.00 min and an initial decay rate of \(6.00 \times 10^{3}\) Bq. (a) What is the decay constant? (b) What will be the decay rate at the end of (i) \(5.00 \mathrm{~min}\), (ii) \(10.0 \mathrm{~min}\) (iii) \(25.0 \mathrm{~min} ?\)

A sample of the radioactive nuclide \({ }^{199} \mathrm{Pt}\) is prepared that has an initial activity of \(7.56 \times 10^{11}\) Bq. (a) 92.4 min after the sample is prepared, the activity has fallen to \(9.45 \times 10^{10} \mathrm{~Bq} .\) What is the half-life of this nuclide? (b) How many radioactive nuclei were initially present in the sample?

Calcium- 47 is a \(\beta^{-}\) emitter with a half-life of 4.5 days. If a bone sample contains \(2.24 \mathrm{~g}\) of this isotope, at what rate will it decay?

Which of the following reactions obey the conservation of baryon number? (a) \(\mathrm{p}+\mathrm{p} \rightarrow \mathrm{p}+\mathrm{e}^{+},\) (b) \(\mathrm{p}+\mathrm{n} \rightarrow 2 \mathrm{e}^{+}+\mathrm{e}^{-}\) (c) \(\mathrm{p} \rightarrow \mathrm{n}+\mathrm{e}^{-}+\bar{\nu}_{\mathrm{e}},(\mathrm{d}) \mathrm{p}+\overline{\mathrm{p}} \rightarrow 2 \gamma\)
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