Question

The atomic mass of lead is 208 and its atomic number is 82 . The atomic mass of bismuth is 209 and its atomic number is \(83 .\) The ratio of neutrons/protons in the atom (1) higher of \(\mathrm{Pb}\) (2) higher of \(\mathrm{Bi}\) (3) same of both (4) none of these

Short answer

The neutron/proton ratio is higher for Pb.

Step-by-step solution

- Find Number of Protons

The atomic number represents the number of protons in an atom. For lead (Pb), the atomic number is 82, so it has 82 protons. For bismuth (Bi), the atomic number is 83, so it has 83 protons.

- Calculate Number of Neutrons

To find the number of neutrons, subtract the atomic number from the atomic mass. For Pb, number of neutrons is 208 - 82 = 126. For Bi, number of neutrons is 209 - 83 = 126.

- Determine Neutron/Proton Ratio

Now, calculate the ratio of neutrons to protons for each element. For Pb, the neutron/proton ratio is \( \frac{126}{82} \approx 1.54 \). For Bi, the neutron/proton ratio is \( \frac{126}{83} \approx 1.52 \).

- Compare Ratios

Compare the neutron/proton ratios of Pb and Bi. Since \( 1.54 > 1.52 \), the neutron/proton ratio is higher for Pb.

Key concepts

Atomic Mass

The concept of atomic mass is crucial in understanding the characteristics of different elements. Atomic mass, also known as atomic weight, is the total mass of protons, neutrons, and electrons in an atom. However, electrons have negligible mass, so atomic mass is primarily the sum of protons and neutrons.

Consider the atomic masses of lead (Pb) and bismuth (Bi) used in the exercise. The atomic mass of Pb is 208, and for Bi, it is 209. These values help determine the number of neutrons, which is essential for figuring out the neutron-proton ratio.

• Atomic Mass of Lead (Pb) = 208
• Atomic Mass of Bismuth (Bi) = 209

By understanding the atomic mass, students can easily calculate the number of neutrons and, subsequently, neutron-proton ratios.

Atomic Number

The atomic number is a fundamental concept in chemistry and physics. It represents the number of protons in the nucleus of an atom. This number also determines the element's identity and its position on the periodic table.

In our exercise, the atomic number of lead (Pb) is 82, and for bismuth (Bi), it is 83. These values directly indicate how many protons are present in each element. The knowledge of the atomic number is essential because it helps calculate the number of neutrons when combined with the atomic mass.

• Atomic Number of Lead (Pb) = 82
• Atomic Number of Bismuth (Bi) = 83

With these atomic numbers, you can understand why lead and bismuth have different neutron-proton ratios.

Neutrons and Protons

Neutrons and protons are the two main subatomic particles found in the nucleus of an atom. Protons have a positive charge, while neutrons are neutral. These particles play a significant role in defining the properties of an element.

To find the number of neutrons in an atom, subtract the atomic number from the atomic mass. For instance:

• Lead (Pb): Number of neutrons = 208 (atomic mass) - 82 (atomic number) = 126
• Bismuth (Bi): Number of neutrons = 209 (atomic mass) - 83 (atomic number) = 126

With the number of neutrons and protons identified, we can calculate the neutron-proton ratio:

• Pb: \( \frac{126}{82} \approx 1.54 \)
• Bi: \( \frac{126}{83} \approx 1.52 \)

The higher neutron-proton ratio in lead compared to bismuth suggests different nuclear stability and radioactive properties, offering deep insights into the element's nature.