In a hydrogen-like atom,the velocity of an electron in the second orbit is $v$. What will be the velocity of the electron in its fifth orbit?

If $E$ and $L$ denote the magnitude of total energy and angular momentum of a revolving electron in the $n^{\text{th}}$ Bohr orbit,then:

The de Broglie wavelength of an electron in the first orbit of Bohr's model is . . . . . . .

The magnetic field at the centre due to the motion of an electron in the first Bohr orbit is $B$. The magnetic field due to the motion of an electron in the second Bohr orbit at the centre will be

The frequency of light emitted,when the electron makes a transition from the level of principal quantum number $n=2$ to the level with $n=1$ is (Take,the ionization energy of hydrogen to be $13.6 \ eV$ and $h \simeq 4 \times 10^{-15} \ eV \cdot s$)

A hydrogen atom, initially in the ground state, is excited by absorbing a photon of wavelength $980 \ \text{\AA}$. The radius of the atom in the excited state, in terms of Bohr radius $a_0$, will be (given $hc = 12500 \ \text{eV-\AA}$). (in $a_0$)