Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu)$. The mass of the muon particle is $207$ times that of an electron and its charge is equal to the charge of an electron. The ionization potential of this hydrogen atom will be ............. $eV$.

In Bohr's model of the hydrogen atom,which of the following pairs of quantities are quantized?

The magnetic moment of an electron due to its orbital motion is proportional to ($n$ = principal quantum number).

In the Bohr model of the hydrogen atom,the electrostatic force on the electron depends on the principal quantum number $n$ as:

An electron in an excited state of $Li^{2+}$ ion has angular momentum $\frac{3 h}{2 \pi}$. The de-Broglie wavelength of the electron in this state is $p \pi a_{0}$ (where, $a_{0} = \text{Bohr radius}$). The value of $p$ is

Four electrons,each of mass $m_{e}$,are in a one-dimensional box of size $L$. Assume that the electrons are non-interacting,obey the Pauli exclusion principle,and are described by standing de Broglie waves confined within the box. Define $\alpha = h^{2} / 8 m_{e} L^{2}$ and $U_{0}$ to be the ground state energy. Then,