To understand the behavior of an electron in a hydrogen atom when energy is supplied, let’s break down the concepts of energy levels and electron transitions. In a hydrogen atom, electrons occupy specific energy levels, or shells, around the nucleus. The first shell (n=1) is the closest to the nucleus and has the lowest energy, while the second shell (n=2) is further away and has higher energy.

Energy Levels in Hydrogen Atom

The energy of an electron in a hydrogen atom can be described using the formula:

E = -13.6 eV/n²

Here, E is the energy of the electron, and n is the principal quantum number representing the shell. For the first shell (n=1), the energy is -13.6 eV, and for the second shell (n=2), it is -3.4 eV. The difference in energy between these two levels is what determines how much energy is required for the electron to transition from the first shell to the second shell.

Energy Required for Transition

The energy required for the electron to jump from the first shell to the second shell can be calculated as follows:

• Energy in the first shell (n=1): -13.6 eV
• Energy in the second shell (n=2): -3.4 eV
• Energy difference (ΔE) = E(n=2) - E(n=1) = -3.4 eV - (-13.6 eV) = 10.2 eV

This means that an energy of 10.2 eV is required for the electron to transition from the first shell to the second shell.

What Happens with Different Energy Supplies?

Now, let’s consider the scenarios based on the energy supplied:

• If energy supplied is less than 10.2 eV: The electron will not have enough energy to overcome the energy barrier and will remain in the first shell.
• If energy supplied is exactly 10.2 eV: The electron will absorb this energy and make the transition to the second shell.
• If energy supplied is more than 10.2 eV: The electron will still jump to the second shell, but the excess energy will not be lost; instead, it can be converted into kinetic energy, causing the electron to move faster in its new orbit.

Understanding Excess Energy

When an electron absorbs energy greater than the minimum required for a transition, it can be thought of as gaining additional kinetic energy. This is similar to how a ball thrown upwards will not only reach a certain height (representing the energy needed to reach a new level) but can also continue to rise if thrown with more force (representing excess energy).

In summary, if the energy supplied is less than the required amount, the electron will not jump to the next shell. However, if the energy supplied is equal to or greater than the required amount, the electron will transition to the second shell, with any excess energy contributing to its kinetic energy in that shell.