Question

What energy photon is necessary to raise an electron in hydrogen from the $\mathrm{n}=1$ to the $\mathrm{n}=3$ energy level?

Answer 1

Bohr's Model of a Hydrogen Atom

• The Bohr model of hydrogen's atomic structure first accurately explained the radiation spectra of atomic hydrogen.
• Bohr’s model of the hydrogen atom is based on three postulates.
• An electron travels in a circular orbit around the nucleus.
• In orbit, an electron's angular momentum is quantized.
• A photon is emitted or absorbed whenever an electron's energy changes when it makes a quantum jump from one orbit to another.

Energy

• The energy is as follows:

$∆\mathrm{E}={\mathrm{E}}_{\mathrm{f}}-{\mathrm{E}}_{\mathrm{i}}$

• $∆\mathrm{E}$ is the energy photon.
• ${\mathrm{E}}_{\mathrm{f}}$ is the final level energy.
• ${\mathrm{E}}_{\mathrm{i}}$ is the initial level energy.
• Energy of nth excited state is, ${\mathrm{E}}_{\mathrm{n}}=\frac{13.6}{{\mathrm{n}}^2}$.
• The energy required to raise an electron in hydrogen from the $\mathrm{n}=1$ to $\mathrm{n}=3$ is as follows:

$\begin{array}{rcl}∆\mathrm{E}& =& {\mathrm{E}}_{\mathrm{f}}-{\mathrm{E}}_{\mathrm{i}}\\ & =& \left(-\frac{13.6}{3^2}\right)-\left(-\frac{13.6}{1^2}\right)\\ & =& -1.51+13.6\\ & =& 12.1\mathrm{eV}\end{array}$

• The required energy is $12.1\mathrm{eV}$.