Question

The energy of an electron in the nth bohr orbit is proportional to

Answer 1

The energy of an electron in the nth Bohr orbit is proportional to Z²/n².

• According to Bohr's model of an atom, electrons revolve around the nucleus in particular orbits.
• The energy of an electron revolving in these orbits is always negative.
• The negative energy shows that the electron belongs to a bounded system.
• The energy is given by the formula $-13.6\frac{z^2}{n^2} eV$.
• Here, z and n are the atomic numbers and the principal quantum number (orbit number) for the given Hydrogen-like atom.

Answer 2

Answer:

The energy of the electron in the nth Bohr orbit is proportional to $\frac{ Z^{2} }{n^{2} }$

Explanation:

The energy of the negatively charged electron in the nth Bohr orbit is given as the following;

E = $\frac{-13.6 Z^{2} }{n^{2} } eV$

Where the Z = the atomic number of the element

n = shell number or orbit number or the principal quantum number.

eV = electron volts

It is negative as the electron is in a bounded system.

As here we can see that -13.6 is a constant term and the energy is thus proportional to $\frac{ Z^{2} }{n^{2} }$

That is the energy is proportional to the ratio of the square of the atomic number of the element divided by the square of its principal quantum number or, the shell number or the orbit number.