The isotopic mass for a particular isotope of gold is 196.9665 amu. The mass number for this gold isotope __.
A) is 79
B) is 196
C) is 197
D) cannot be determined from the information given
The correct answer and explanation is :
The correct answer is:
C) is 197
Explanation:
To understand the relationship between the isotopic mass and the mass number, let’s break it down:
- Isotopic Mass: The isotopic mass is the weighted average mass of an isotope of an element. It is measured in atomic mass units (amu). In this case, the isotopic mass of the gold isotope is 196.9665 amu.
- Mass Number: The mass number is the sum of the protons and neutrons in the nucleus of an atom. It is always a whole number. It does not include electrons because they have a negligible mass compared to protons and neutrons.
The atomic number of gold (Au) is 79, which means it has 79 protons. Since isotopes of an element differ in the number of neutrons, the mass number will vary.
To calculate the mass number, we use the fact that it is approximately equal to the sum of the protons and neutrons in the nucleus. For gold, the atomic number (number of protons) is 79. Therefore, the number of neutrons would be:
[
\text{Neutrons} = \text{Mass Number} – \text{Protons}
]
Given that the isotopic mass is close to 197 amu (196.9665 amu), we can deduce that the isotope with a mass of approximately 197 amu has a mass number of 197.
This is because isotopic masses are generally close to the mass number, with a small fractional difference due to the binding energy of the nucleus and the fact that atomic mass is a weighted average of all isotopes of the element.
Summary:
The mass number for this gold isotope is 197, which corresponds to choice C.
