What is the change in angular momentum of an electron in a hydrogen atom when it transitions from the $4^{th}$ orbit to the $5^{th}$ orbit? $(h = 6.6 \times 10^{-34} \, J \cdot s)$

Imagine removing one electron from $He^4$ and $He^3$. Their energy levels,as worked out on the basis of the Bohr model,will be very close. Explain why?

$A$ hydrogen atom,a deuteron atom,a $He^+$ ion,and a $Li^{++}$ ion each contain a single electron orbiting their nucleus. The wavelengths of the electromagnetic radiation emitted during the transition of the electron from the $n = 2$ orbit to the $n = 1$ orbit are found to be $\lambda_1, \lambda_2, \lambda_3$,and $\lambda_4$ respectively. Then:

The de-Broglie wavelength of the electron in the ground state of the hydrogen atom is ..... (radius of the first orbit of hydrogen atom $= 0.53 \ \text{Å}$). (in $\text{Å}$)

Apply Bohr's atomic model to a lithium atom. Assuming that its two $K$-shell electrons are so close to the nucleus that the nucleus and the $K$-shell electrons act as a core with an effective positive charge equivalent to $1e$. The ionization energy of its outermost electron is......$eV$.

An electron in the hydrogen atom initially in the fourth excited state makes a transition to $n^{\text{th}}$ energy state by emitting a photon of energy $2.86 \ eV$. The integer value of $n$ will be . . . . . . .