Question

The energy of the electron in the nth orbit of hydrogen atom is given as:
$E_n=-{\displaystyle \frac{1311.8}{n^2}}KJmo{l}^{-1}$
What is the energy emitted per atom when an electron jumps from third energy level to second energy level?

Answer 1

Hint: In order to find the energy emitted per atom,we are given the energy of electrons in the first orbit as -13.6eV. So with the help of the given data and Bohr’s theory we can find the energy of the second orbit as well as the third orbit and at last we’ll find the difference between them. That will give us our required answer.

Complete answer:
After the failure of Thomson’s and Rutherford’s model several other chemists tried to explain the structure of an atom. One of the best models was explained by Niels Bohr.
Via Bohr’s model, we were able to calculate the energy, radius, and many other things of atoms.
As from Bohr’s theory of an atom,
The energy of an electron in the first orbit is given as $-13.6eV$ .
From Bohr’s theory, we also know that the energy is given by $E\propto {\displaystyle \frac{Z^2}{n^2}}$ , where E is energy, Z is nuclear charge and n is orbit number.
Thus, energy of the second orbit is $={\displaystyle \frac{-13.6}{{(2)}^2}}eV={\displaystyle \frac{-13.6}{4}}eV$
And the energy of the third orbit is $={\displaystyle \frac{-13.6}{{(3)}^2}}eV={\displaystyle \frac{-13.6}{9}}eV$
The change in energy is given by $\mathrm{\Delta }E=-13.6\left({\displaystyle \frac{1}{9}}-{\displaystyle \frac{1}{4}}\right)\times 1.6\times {10}^{-19}$
Or $\mathrm{\Delta }E=3.022\times {10}^{-19}Jat{m}^{-1}$

Additional Information: In the early nineteenth century, the chemists were interested in knowing the actual structure of that minute particle which is the building block of everything which is said to be an atom. When two or atoms combine together they form a molecule. The earliest known attempt to present such a model was done by J.J Thomson. However, the best-explained model was Bohr’s model which has some limitations.

Note:
Bohr’s atomic theory was a game-changer but the theory has some limitations which are as follows: - (i) this theory fails in explaining the hydrogen spectrum observed in spectroscopy, (ii) this theory fails in explaining the spectra of multi-electron species, (iii) this theory fails in explaining the Zeeman effect, (iv) this theory fails in explaining the stark effect, (v) this theory fails in explaining the shape of molecules, (vi) this theory fails in explaining the dual nature of matter.