Bohr's model of the hydrogen atom: quantization of electronic structure

Bohr’s model of the hydrogen atom started from the planetary model, 

but he added one assumption regarding the electrons. 

What if the electronic structure of the atom was quantized? Bohr suggested that the perhaps the electrons could only orbit the nucleus in specific orbits or shells with a fixed radius. Only shells with a radius given by the equation below would be allowed, and the electron could not exist in between these shells. Mathematically, we could write the allowed values of the atomic radius as $\mathrm{ <b>\; r</b>}$(n)=n2⋅r(1)r(n)=n^2\cdot r(1)r(n)=n​2​​⋅r(1)r, left parenthesis, n, right parenthesis, equals, n, start superscript, 2, end superscript, dot, r, left parenthesis, 1, right parenthesis,

where $n$nn is a positive integer, and $r(1)$r(1)r, left parenthesis, 1, right parenthesis is the Bohr radius, the smallest allowed radius for hydrogen.

He found that $r(1)$r(1)r, left parenthesis, 1, right parenthesis has the value

$\text{Bohr radius}=r\left(1\right)=0\mathrm{.}529\times 10^{-10}\text{m}$
$\text{Bohr radius}=r(1)=0.529 \times 10^{-10} \,\text{m}$By keeping the electrons in circular, quantized orbits around the positively-charged nucleus, Bohr was able to calculate the energy of an electron in the $n$nnth energy level of hydrogen: $E(n)=-\dfrac{1}{n^2} \cdot 13.6\,\text{eV}$E(n)=−​n​2​​​​1​​⋅13.6eVE, left parenthesis, n, right parenthesis, equals, minus, start fraction, 1, divided by, n, start superscript, 2, end superscript, end fraction, dot, 13, point, 6, space, e, V, where the lowest possible energy or ground state energy of a hydrogen electron—$E(1)$E(1)E, left parenthesis, 1, right parenthesis—is $-13.6\,\text{eV}$−13.6eVminus, 13, point, 6, space, e, V. Bohr radius=r(1)=0.529×10​−10​​m




Note that the energy is always going to be a negative number, and the ground state, $n=1$n=1n, equals, 1, has the most negative value. This is because the energy of an electron in orbit is relative to the energy of an electron that has been completely separated from its nucleus, $n=\infty$n=∞n, equals, infinity, which is defined to have an energy of $0\,\text{eV}$0eV0, space, e, V. Since an electron in orbit around the nucleus is more stable than an electron that is infinitely far away from its nucleus, the energy of an electron in orbit is always negative.