Structure of Atom

KE_max = hc/λ - φ = 6.63e-19 - 4.41e-19 = 2.22e-19 = 222e-21 J.

For n=4, l can be 0,1,2,3. m=-2 is possible for l=2,3. So 2 subshells (4d, 4f).

1, 2 and 3 are according to quantum theory but (4) is statement of kinetic theory of gases

Kindly consider the following figure

Probability density of plots

From the given graph answer is (1)

$\mathrm{}\bar{v}=\frac{1}{\lambda }={\mathrm{R}\mathrm{z}}^2?\left(\frac{1}{{\mathrm{n}}_1^2}-\frac{1}{{\mathrm{n}}_2^2}\right)$

For $\mathrm{H}$ atom $\mathrm{z}=1$

$\bar{v}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

For Balmer series:  ${\mathrm{n}}_1=2$

If ${\mathrm{n}}_2=3\therefore \frac{1}{\lambda }={\mathrm{R}\mathrm{z}}^2\left(\frac{1}{4}-\frac{1}{9}\right)$

$\frac{1}{\lambda }=\mathrm{R}\frac{5}{36}$

${\lambda }_{\mathrm{m}\mathrm{a}\mathrm{x}}=\frac{36}{5\mathrm{R}}$

In a hydrogen atom, which we know has a single electron, the orbital energy will only depend on the principal quantum number (n). Here, the orbitals like 2s and 2p have the same energy (degenerate).

It's a little different with multielectron atoms. The energy depends on both n and the azimuthal quantum number (l). This causes splitting. And, the energies increase in the order: s < p < d < f.