Question

How did quantum mechanics change the Bohr model of the atom?

Answer 1

According to Bohr’s model of atom the nucleus is positively charged surrounded by negatively charged electrons. It explains how electrons do not lose energy while revolving around the nucleus and hence remain stable. Quantum mechanics helps in explaining the stability of atoms.

Complete answer:
Before Bohr's model of atom, Rutherford’s model of atom failed to account for the stability of an electron in its orbit. But the Bohr’s model of the atom explained the stability of an electron in its orbit using quantum mechanics.
The Bohr’s model of atom paints the picture of an atom as containing a positively charged nucleus in the centre with negatively charged electrons revolving around it.
It also explains that electrons can only revolve in specific orbits which have an angular momentum as multiples of $\dfrac{h}{2\pi }$. Therefore, momentum of possible orbits is given by-
$L=\dfrac{nh}{2\pi }$
Here, $L$ is the angular momentum of the orbit
$n$ is an integer
$h$ is the Rydberg’s constant
Also, the electrons in these orbits have fixed energy, as the shells increase, the energy of the electron also increases and vice versa. The energy of these electrons is also determined using quantum mechanics and is given by-
$E=-13.6\dfrac{{{z}^{2}}}{{{n}^{2}}}$
Here, $E$ is the energy of an electron in an orbit
$z$ is the atomic number
$n$ I the number of orbit
Therefore, the Bohr’s orbit uses quantum mechanics to describe the energy o f an electron in its orbit and to explain its stability.

Note:
The Bohr’s orbit is only applicable for hydrogen like species. Orbits can also be called energy levels. The highest energy is the energy of an electron at infinity. The energy of an electron in an orbit is always negative because it is the potential energy due to the attractive force of the nucleus.