The ground state energy of a hydrogen atom is \(-13.6~\text{eV}\). The energy needed to ionize the hydrogen atom from its second excited state will be:
1. \(13.6~\text{eV}\)
2. \(6.8~\text{eV}\)
3. \(1.51~\text{eV}\)
4. \(3.4~\text{eV}\)

Let \(L_1\) and \(L_2\) be the orbital angular momentum of an electron in the first and second excited states of the hydrogen atom, respectively. According to Bohr's model, the ratio \(L_1:L_2\) is:
1. \(1:2\)
2. \(2:1\)
3. \(3:2\)
4. \(2:3\)

In which of the following systems will the radius of the first orbit (n = 1) be minimum:

1. doubly ionized lithium

2. singly ionized helium

3. deuterium atom

4. hydrogen atom

If the energy of the hydrogen atom in $n^{th}$ orbit is $E_n$, then the energy in $n^{th}$ orbit of the singly ionised helium atom will be:
1.  4$E_n$
2.  $E_n$/4
3.  2$E_n$
4.  $E_n$/2