In hydrogen atom, the minimum energy required to excite an electron from $2^{\mathrm{nd} }$ orbit to the  $3^{\mathrm{rd} }$ orbit is

According to Bohr's theory the amount of energy required to excite an electron from one orbit to another orbit is given by the difference in energy between those two orbits.

$∆\mathrm{E} = 13.6 {\mathrm{Z}}^2 \left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right) \mathrm{eV}$

Here for H-atom $\mathrm{Z}=1 {\mathrm{n}}_1=2 \mathrm{and} {\mathrm{n}}_2=3$

$$\begin{gathered} ∆\mathrm{E} = 13.6 \left(\frac{1}{2^2}-\frac{1}{3^2}\right) \mathrm{eV} \\ ∆\mathrm{E} = 13.6 \left(\frac{1}{4}-\frac{1}{9}\right) \mathrm{eV} \\ ∆\mathrm{E} = 13.6 \times \frac{5}{36}\mathrm{eV} = 1.9 \mathrm{eV} \end{gathered}$$