Questions: In the energy expression for hydrogen-like atoms, Z is equal to the: Select the correct answer below: atomic mass charge on the electron mass of the electron nuclear charge

In the energy expression for hydrogen-like atoms, Z is equal to the:

Select the correct answer below:
atomic mass
charge on the electron
mass of the electron
nuclear charge

Transcript text: Question In the energy expression for hydrogen-like atoms, $Z$ is equal to the: Select the correct answer below: atomic mass charge on the electron mass of the electron nuclear charge

Solution

Solution Steps

Step 1: Understand the Context

In the context of hydrogen-like atoms, the energy expression typically refers to the energy levels of an electron in an atom with only one electron, similar to the hydrogen atom. The formula for the energy levels is given by:

\[ E_n = -\frac{Z^2 \cdot R_H}{n^2} \]

where $E_n$ is the energy of the electron at level $n$, $Z$ is the atomic number (nuclear charge), $R_H$ is the Rydberg constant, and $n$ is the principal quantum number.

Step 2: Identify the Role of $Z$

In the formula, $Z$ represents the nuclear charge, which is the number of protons in the nucleus of the atom. This is because the energy levels depend on the strength of the electrostatic attraction between the nucleus and the electron, which is determined by the number of protons.

Step 3: Evaluate the Options

Atomic mass: This is not related to the energy expression for hydrogen-like atoms.
Charge on the electron: This is a constant and does not vary with different atoms.
Mass of the electron: This is also a constant and does not represent $Z$.
Nuclear charge: This is the correct representation of $Z$ in the energy expression.