A positron is emitted from \(\mathrm{Na}^{23}\) The ratio of the atomic mass and atomie number in the resulting nuclide is (a) \(\frac{22}{10}\) (b) \(\frac{22}{11}\) (c) \(\frac{23}{10}\) (d) \(\frac{23}{12}\)

Short Answer

Expert verified
The ratio of the atomic mass and atomic number in the resulting nuclide is \(\frac{23}{10}\) (c).

Step by step solution

01

Understanding Positron Emission

Positron emission is a type of beta decay where a proton in the nucleus is converted into a neutron with the release of a positron (beta plus particle) and a neutrino. The atomic number (number of protons, Z) decreases by one, but the atomic mass number (total number of protons and neutrons, A) remains the same.
02

Identify Initial Nuclide

Begin by identifying the initial nuclide, which is sodium with the symbol \(\mathrm{Na}^{23}\). This implies it has an atomic number of 11 (since Na is the 11th element on the periodic table) and an atomic mass number of 23.
03

Determine Resulting Nuclide After Positron Emission

Since a positron is emitted, the atomic number will decrease by 1, becoming 10, while the atomic mass number will remain unchanged at 23.
04

Calculate the Ratio

After emission, the resulting nuclide has an atomic mass number (A) of 23 and an atomic number (Z) of 10. The ratio of the atomic mass to atomic number is therefore \(\frac{23}{10}\).

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Key Concepts

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

Beta Decay
Beta decay is a nuclear process where an unstable atom releases energy to become more stable. One type of beta decay is 'positron emission', which involves a proton transforming into a neutron, an anti-electron (also called a positron), and a neutrino. This transformation leads to the emission of the positron from the nucleus. Importantly, the atomic mass number, which totals the number of protons and neutrons, stays constant during positron emission; however, the atomic number, representing the number of protons, decreases by one.

When explaining beta decay, it's crucial to understand that it occurs in isotopes with an unstable ratio of neutrons to protons. The positron emission helps to balance this ratio and leads the nuclide towards stability. This process is accompanied by a change in the nucleus's composition but not its overall mass.
Atomic Mass
The term 'atomic mass' is a fundamental concept in the study of chemistry and physics. It refers to the mass of an atom, typically measured in atomic mass units (amu). The atomic mass is roughly the sum of the masses of the protons and neutrons in the atomic nucleus since the mass of electrons is substantially less and often negligible in comparison.

An important characteristic of atomic mass is that it remains unchanged during positron emission. This is because the process only involves the conversion of a proton into a neutron, with both particles having approximately equal mass. Since the number of particles (protons and neutrons) in the nucleus remains constant, so does the atomic mass.
Atomic Number
Another central concept in understanding atomic structure is the 'atomic number'. This number symbolizes the quantity of protons found within an atom's nucleus and effectively defines the chemical element. For instance, every atom with 11 protons is an atom of sodium (Na), regardless of how many neutrons may be present.

In the context of positron emission, the atomic number decreases because a proton is converted into a neutron. This transformation leads to the creation of a different element altogether. It's important to highlight this to students, as changes in atomic number during nuclear reactions result in the transmutation of elements, which is a cornerstone concept in nuclear chemistry.
Nuclide
The term 'nuclide' refers to a distinct species of an atom, characterized by its number of protons, neutrons, and energy state. A nuclide is defined not just by its atomic number, but also by its atomic mass number, which includes both protons and neutrons. It is key to distinguish between 'nuclide' and 'isotope', as isotopes are nuclides of the same element differing only in neutron number, whereas nuclides can refer to any atomic nucleus identity.

Nuclides are symbolically represented by the element's symbol followed by the atomic mass number, as in \(\mathrm{Na}^{23}\). When nuclides go through positron emission, while their atomic mass stays the same, the atomic number and consequently the nuclide itself changes, leading to the formation of a new nuclide with different properties.

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