JEE Main 2023 — Structure Of Atom Question with Solution

The energy of an electron in a hydrogen atom is given by the following formula:

$$E_n=\frac{-13.6\mathrm{eV}}{n^2}$$

where n is the principal quantum number (Bohr orbit number). To find the energy in the third Bohr orbit (n = 3), we can use the formula:

$$E_3=\frac{-13.6\mathrm{eV}}{3^2}=\frac{-13.6\mathrm{eV}}{9}$$

Now, we are given the energy of the electron in the first Bohr orbit (n = 1):

$$E_1=-2.18\times 10^{-18}\mathrm{J}$$

First, let's convert this energy to electron volts (eV):

$$E_1=-2.18\times 10^{-18}\mathrm{J}\times \frac{1\mathrm{eV}}{1.6\times 10^{-19}\mathrm{J}}\approx -13.6\mathrm{eV}$$

Now we can find the ratio of $$E_3$$ to $$E_1$$:

$$\text{Ratio}=\frac{E_3}{E_1}=\frac{-\frac{13.6\mathrm{eV}}{9}}{-13.6\mathrm{eV}}=\frac{1}{9}$$

Thus, the energy of the electron in the third Bohr orbit is $$\frac{1}{9}$$ th of its energy in the first Bohr orbit.