To accommodate the view that matter is made up to $5$ elements only, a scientist proposed the following hypothesis; that atoms can have a maximum principal quantum number $n _{\operatorname{man}}$ and no higher. Then, which of the following statements must be true ?
$n _{\max }=1$, and electrons have spin
$n _{\max }=2$, and electrons have spinless but nevertheless obey the Pauli Exclusion principle.
$n_{\max }=3$, and electrons are spinless but nevertheless obey the Pauli Exclusion principle.
$n_{\max }=4$, and electrons have spin
The first line in the Lyman series has wavelength $\lambda $ . The wavlength of the first line in Balmer series is
Which one did Rutherford consider to be supported by the results of experiments in which $\alpha - $ particles were scattered by gold foil?
A proton is fired from very far away towards a nucleus with charge $Q=120 \ e$, where $e$ is the electronic charge. It makes a closest approach of $10 \ fm$ to the nucleus. The de Brogle wavelength (in units of $fm$ ) of the proton at its start is :
(take the proton mass, $m _0=(5 / 3) \times 10^{-27} kg , h / e =4.2 \times 10^{-15} J / s / C ; \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 m / F ; 1 fm =10^{-15} m$ )
Ionization potential of hydrogen atom is $13.6 V$. Hydrogen atoms in the ground state are excited by monochromatic radiation of photon energy $12.1 eV.$ The spectral lines emitted by hydrogen atoms according to Bohr's theory will be
Hydrogen $(H)$, deuterium $(D)$, singly ionized helium $(H{e^ + })$ and doubly ionized lithium $(Li)$ all have one electron around the nucleus. Consider $n =2$ to $n = 1 $ transition. The wavelengths of emitted radiations are ${\lambda _1},\;{\lambda _2},\;{\lambda _3}$ and ${\lambda _4}$ respectively. Then approximately