Question

Among the isotopes of all the elements (only non-radioactive), the \(n / p\) ratio is maximum for (a) \(\mathrm{H}^{1}\) (b) \({ }_{1} \mathrm{H}^{3}\) (c) \({ }_{83} \mathrm{Bi}^{209}\) (d) \({ }_{2} \mathrm{He}^{4}\)

Short answer

The n/p ratio is maximum for {}_{1}\mathrm{H}^{3} (H-3).

Step-by-step solution

Understanding the n/p ratio

The n/p ratio represents the ratio of the number of neutrons (n) to the number of protons (p) in an atom's nucleus. For a given isotope, this ratio can be calculated by subtracting the atomic number (which represents the number of protons) from the mass number (which represents the total number of protons and neutrons).

Calculating the n/p ratio for each isotope

Calculate the n/p ratio for each given isotope by using the formula: n/p = (mass number - atomic number) / atomic number.For H-1: n/p = (1 - 1) / 1 = 0/1 = 0.For H-3: n/p = (3 - 1) / 1 = 2/1 = 2.For Bi-209: n/p = (209 - 83) / 83 = 126/83 ≈ 1.52.For He-4: n/p = (4 - 2) / 2 = 2/2 = 1.

Comparing the n/p ratios

Compare the n/p ratios calculated in Step 2. The isotope with the highest n/p ratio is H-3 with a ratio of 2. The other isotopes have lower n/p ratios.

Key concepts

Neutron to Proton Ratio

The neutron to proton ratio, often represented as the n/p ratio, is fundamental in understanding the stability and characteristics of an atom's nucleus. This ratio is particularly insightful when studying isotopes, which are variations of elements with the same number of protons but different numbers of neutrons. A higher n/p ratio suggests more neutrons than protons, which is a distinctive feature in certain isotopes and can have implications for the atom's stability.

For non-radioactive isotopes, maintaining a balanced n/p ratio is indicative of nuclear stability. As you saw in the exercise, calculating the n/p ratio involves subtracting the atomic number from the mass number and then dividing the result by the atomic number. The isotope with the higher n/p ratio among the options provided is H-3 (Tritium), with a ratio of 2, indicating this isotope has twice as many neutrons as protons.

Isotopes Calculation

Isotopes calculation extends far beyond just understanding the n/p ratio—it includes comprehending how isotopes differ from one another and predicting their behavior. Isotopes of an element have the same atomic number (number of protons) but vary in their mass number due to the differing number of neutrons. This is crucial for physical and chemical properties such as atomic mass and nuclear stability. When you calculate the mass number of an isotope, as mentioned in the step-by-step solution, you're in essence totaling the number of protons and neutrons within the nucleus.

More Than Just Mass:

While the mass of an isotope is its most obvious difference, isotopes can also show variations in nuclear spin and energy levels. These differences are pivotal in applications ranging from medical diagnostic imaging to nuclear energy production.

Atomic Number

The atomic number is a cardinal concept in chemistry and physics, acting as a unique identifier for each chemical element. Represented as 'Z', the atomic number indicates the number of protons found in the nucleus of an atom, which determines the element's identity. It's also indirectly tied to the arrangement of electrons in an atom, hence shaping the chemical behavior of the element.

In the exercise provided, the atomic numbers were crucial in calculating the n/p ratio since it gave us the starting point to find out how many neutrons were present in each isotope. This sheds light on why the atomic number is one of the first things you learn in a chemistry class: understanding it is essential to comprehending the whole periodic table and the behavior of elements.

Mass Number

The mass number, denoted as 'A', is the sum total of protons and neutrons in the nucleus of an atom. Unlike the atomic number, the mass number isn't fixed for a particular element because it varies with different isotopes. To find the mass number, simply add the number of protons (atomic number) to the number of neutrons. This figure is critical for identifying specific isotopes and understanding their properties.

Referring back to the provided exercise, the mass number is integral in determining the n/p ratio. Elements with a higher mass number than their atomic number possess a greater number of neutrons, which corresponds to a higher n/p ratio. This number is also essential when discussing atomic mass units and calculating molar masses for substances, making it indispensable for stoichiometry and other quantitative aspects in chemistry.