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Chapter 45: Problem 20

What element has 11 protons and 12 neutrons? [Hint: What is the value of \(A\) ?]

Short Answer

Expert verified
The element is sodium (Na).

Step by step solution

01

Understand the atomic number

The atomic number, represented by the letter \( Z \), is the number of protons in an atom. It is used to identify the element. Here, the atomic number is 11, which corresponds to the element sodium (Na) on the periodic table.
02

Calculate the atomic mass

The atomic mass, denoted by \( A \), is the sum of the number of protons \( Z \) and neutrons \( N \) in the nucleus. Thus, \( A = Z + N = 11 + 12 = 23 \).
03

Identify the element

With an atomic number of 11 and an atomic mass of 23, the element on the periodic table is sodium (Na). Sodium is the only element with these characteristics.

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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 fascinating part of atomic structure. It is symbolized by the letter \( Z \) and represents the number of protons in an atom. This number is crucial because it determines the identity of an element. Just like our unique fingerprints, every element has its own atomic number. For example, if an atom has 11 protons, its atomic number is 11. This atomic number directly corresponds to the element's position on the periodic table.
  • In our example, an atomic number of 11 corresponds to sodium (Na).
  • Each different atomic number represents a different element.
  • No two elements can have the same atomic number.
By knowing the atomic number, you can easily find the element on the periodic table. This is why the atomic number is often used as a starting point to determine what element you are dealing with.
Atomic Mass
Atomic mass is a slightly more complex concept but equally essential in atomic structure. Represented by the letter \( A \), atomic mass is the total number of protons and neutrons in an atom's nucleus. Think of it like the total weight of the nucleus. To calculate atomic mass, you add together the number of protons and the number of neutrons:
\[ A = Z + N \]
  • Where \( A \) is the atomic mass, \( Z \) is the number of protons, and \( N \) is the number of neutrons.
  • For our sodium example: \( A = 11 + 12 = 23 \).
This number often appears as a decimal on the periodic table due to the existence of isotopes, which are atoms with the same number of protons but different numbers of neutrons. Understanding atomic mass is essential because it gives you insights into the structure and stability of the atom.
Protons and Neutrons
In the core of an atom, the nucleus, you'll find protons and neutrons together. These two particles make up almost the entire atomic mass. Let鈥檚 dive into each of them:
  • Protons: Protons are positively charged particles found within the nucleus. They determine the atomic number \( Z \) and, therefore, the identity of the element.
  • Neutrons: Neutrons are neutral. They have no charge but have a similar mass to protons. Neutrons contribute to the atomic mass \( A \) but do not affect the atomic number.
Together, they form the dense core of the atom, which accounts for nearly all of its mass. The balance and number of these particles are vital. An imbalance can lead to isotopes or even unstable atoms.

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Most popular questions from this chapter

Technetium-99 (忙?r) has an excited state that decays by emission of a gamma ray. The half-life of the excited state is 360 min. What is the activity, in curies, of \(1.00 \mathrm{mg}\) of this excited isotope? Because we have the half-life \(\left(t_{1 / 2}\right)\) we can determine the decay constant since \(\lambda t_{1 / 2}=0.693 .\) The activity of a sample is \(\lambda N .\) In this case, $$ \lambda=\frac{0.693}{t_{1 / 2}}=\frac{0.693}{21600 \mathrm{~s}}=3.21 \times 10^{-5} \mathrm{~s}^{-1} $$ We also know that \(99.0 \mathrm{~kg}\) of Tc contains \(6.02 \times 10^{26}\) atoms. A mass \(m\) will therefore contain \([m /(99.0 \mathrm{~kg})]\left(6.02 \times 10^{26}\right)\) atoms. In our case, \(m=1.00 \times 10^{-6} \mathrm{~kg}\), and so $$ \begin{aligned} \text { Activity } &=\lambda N=\left(3.21 \times 10^{-5} \mathrm{~s}^{-1}\right)\left(\frac{1.00 \times 10^{-6} \mathrm{~kg}}{99.0 \mathrm{~kg}}\right)\left(6.02 \times 10^{26}\right) \\ &=1.95 \times 10^{14} \mathrm{~s}^{-1}=1.95 \times 10^{14} \mathrm{~Bq} \end{aligned} $$

A certain isotope has a half-life of \(7.0 \mathrm{~h}\). How many seconds does it take for 10 percent of the sample to decay?

Cesium-124 has a half-life of \(31 \mathrm{~s}\). What fraction of a cesium124 sample will remain after \(0.10 \mathrm{~h}\) ?

How many neutrons are in the nucleus of \({ }^{14} \mathrm{C}\) ? Is this the common form of carbon? How many neutrons does "ordinary" carbon have? [Hint: What is the value of \(A\) ?]

Uranium-238 \(\left({ }_{92}^{238} \mathrm{U}\right)\) ) is radioactive and decays into a succession of different elements. The following particles are emitted before the nucleus reaches a stable form: \(\alpha, \beta, \beta, \alpha, \alpha, \alpha, \alpha, \alpha, \beta, \beta, \alpha, \beta\), \(\beta\), and \(\alpha\left(\beta\right.\) stands for "beta particle, \(" e^{-}\) ). What is the final stable nucleus? The original nucleus emitted 8 alpha particles and 6 beta particles. When an alpha particle is emitted, \(Z\) decreases by 2 , since the alpha particle carries away a charge of \(+2 e\). A beta particle carries away a charge of \(-1 e\), and so as a result the charge on the nucleus must increase to \((Z+1) e\). We then have, for the final nucleus, Final \(Z=92+6-(2)(8)=82\) Final \(A=238-(6)(0)-(8)(4)=206\) The final stable nucleus is \({ }_{82}^{206} \mathrm{~Pb}\) -
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