Physics Question on atom structure models

Question

In a hypothetical Bohr hydrogen atom, if the mass of the electron is double then the energy of the electron in the first orbit is:

Answer 1

Solution

The correct option is: (A): -27.2 eV.

In a hypothetical Bohr hydrogen atom, the energy levels of the electron are quantized, and they are given by the formula:

E = -13.6 eV / n^2

Where:

E is the energy of the electron level
n is the principal quantum number of the orbit

The energy of the electron in the first orbit (n = 1) can be calculated using this formula as:

E1 = -13.6 eV / (1^2) = -13.6 eV

Now, if the mass of the electron is doubled while keeping the other parameters constant, it implies that the reduced mass in the expression for kinetic energy will change, but the electrostatic force between the electron and the nucleus remains unchanged (since it's based on the charge of the electron). The energy levels in the hydrogen atom are determined by a balance between the kinetic and potential energies.

If the mass of the electron is doubled, its kinetic energy will also double, which means the total energy of the electron in the first orbit will change. Since the energy is inversely proportional to the square of the principal quantum number, doubling the energy would result in a new energy value of -27.2 eV.

Therefore, the answer of -27.2 eV is justified