Question

It is known that atom contain protons, neutrons and electrons. If the mass of neutron is assumed to half of its original value whereas that of proton is assumed to be twice of its original value then the atomic mass of \({ }_{6}^{14} \mathrm{C}\) will be: \(\quad \hat{\mathbf{v}}\) (a) same (b) \(14.28 \%\) less (c) \(14.28 \%\) more (d) \(28.56 \%\) less

Short answer

14.28% more.

Step-by-step solution

- Understanding the concept of atomic mass

The atomic mass of an element is the sum of the masses of protons, neutrons, and electrons present in the atom. As electrons contribute negligibly to the mass of the atom, they can be ignored in this calculation. Therefore, the atomic mass is mainly the sum of the masses of protons and neutrons.

- Original atomic mass of Carbon-14

In an atom of Carbon-14 (_{}^{14}C), there are 6 protons and 8 neutrons (since atomic number 6 denotes the number of protons, and mass number 14 is the sum of protons and neutrons). Assuming the original mass of each proton and neutron to be 1 unit (to simplify), the original atomic mass of Carbon-14 is 6 (protons) + 8 (neutrons) = 14 units.

- New atomic mass with altered proton and neutron masses

With the changed assumptions, the mass of each neutron is half of its original value (0.5 units) and the mass of each proton is twice its original value (2 units). Now, the new atomic mass will be 6 protons \(\times\) 2 units/proton + 8 neutrons \(\times\) 0.5 units/neutron = 12 units + 4 units = 16 units.

- Calculating the percent change in atomic mass

To calculate the percent change, we take the difference between the new atomic mass and the original atomic mass, divide by the original atomic mass, and multiply by 100. That is \((\frac{16 - 14}{14}) \times 100\% = (\frac{2}{14}) \times 100\% = 14.28\%\).

- Identifying the direction of the change

Since the new atomic mass (16 units) is greater than the original atomic mass (14 units), the atomic mass of Carbon-14 has increased by 14.28%. Hence, the atomic mass is 14.28% more.

Key concepts

Physical Chemistry JEE

Physical Chemistry is an essential component of the JEE (Joint Entrance Examination) syllabus, which challenges students with problems related to the structure of matter down to the atomic level. When it comes to atomic mass calculations, understanding how atomic mass relates to isotopes, nuclear composition, and stoichiometry is crucial.

For effective preparation for JEE, it's important to grasp concepts such as atomic structure, molecular mass, and the periodic table's implications on these calculations. Atomic mass adjustments, like the one described in the exercise, provide excellent practice in manipulating atomic weights and understanding their impact on chemical behavior.

Protons and Neutrons in Atoms

Atoms are the building blocks of matter, consisting of a nucleus that holds protons and neutrons, with electrons orbiting around it. The number of protons, or the atomic number, defines the element, while the total number of protons and neutrons gives us the mass number.

In education and practical work, protons and neutrons are often assumed to have approximately the same mass, typically about 1 atomic mass unit (amu). However, the precise mass of a proton is slightly less than that of a neutron. Nonetheless, in many calculations we simplify, treating each as 1 unit for ease of computation as seen in the exercise provided. Understanding this simplification is pivotal for making quick estimations and for carrying out more complex physical chemistry calculations.

Isotopes and Atomic Mass

Isotopes are forms of the same element that have the same number of protons but different numbers of neutrons. This variance in neutron count affects the atomic mass of the isotope. The atomic mass of an element listed on the periodic table is a weighted average of all naturally occurring isotopes.

When we calculate the atomic mass of an isotope, we sum the masses of protons and neutrons, as electrons have a negligible mass. In the exercise, we analyzed how altering the neutron's and proton’s assumed masses affects Carbon-14's atomic mass. This kind of problem not only reinforces an understanding of isotopes and their masses but also exemplifies how altering fundamental properties can shift atomic weights, an essential concept in isotope chemistry.