Let's solve this step-by-step.
1. Identify the given information:
- The nuclide has 49 protons.
- The nuclide has 62 neutrons.
2. Calculate the mass number (A):
The mass number is the sum of the number of protons and neutrons.
[tex]\[
\text{Mass number} = \text{Number of protons} + \text{Number of neutrons}
\][/tex]
Substituting the given values:
[tex]\[
\text{Mass number} = 49 + 62 = 111
\][/tex]
3. Write the symbol of the nuclide:
The symbol of a nuclide is written in the format [tex]\({}^{A}_{Z} \text{Element}\)[/tex], where:
- [tex]\(A\)[/tex] is the mass number (111 in this case)
- [tex]\(Z\)[/tex] is the atomic number (which is the number of protons, 49 in this case)
- The chemical symbol of the element with atomic number 49 is Indium, which is denoted by "In".
Hence, combining all these, the symbol of the nuclide is:
[tex]\[
{}_{49}^{111}\text{In}
\][/tex]
Now, let's compare our derived symbol with the provided options:
- [tex]\( \frac{49}{42} \)[/tex] in: This is not correct because the numbers do not align with protons and mass number.
- [tex]\( 62 \ln \)[/tex]: This is incorrect because it does not reflect the format [tex]\({}^{A}_{Z} \text{Element}\)[/tex] and "62" is not the atomic number.
- [tex]\({ }_{111}^{49} \text{In}\)[/tex]: This is reversed, incorrect alignment of mass and atomic numbers.
- [tex]\(\underset{49}{111} \ln\)[/tex]: This is almost correct but there is an error in the formatting of the element symbol "In" (Indium).
The accurate symbol for the nuclide given the numbers should be:
[tex]\[
{}_{49}^{111}\text{In}
\][/tex]
Thus, this correctly formatted choice matches the derived symbol from the data provided.
