If the atom $_{100}F{m^{257}}$ follows the Bohr model and the radius of $_{100}F{m^{257}}$ is $n$ times the Bohr radius, then find $n$

An $\alpha$- particle of $5\ MeV$ energy strikes with a nucleus of uranium at stationary at an scattering angle of $180^o$. The nearest distance upto which $\alpha$- particle reaches the nucleus will be of the order of

The wavelength of the first line of Balmer series of hydrogen atom is $\lambda \,\mathop A\limits^o $. The wavelength of this line of a double ionised lithium atom $(Z = 3)$is

Consider the following statements:

$I$. All isotopes of an element have the same number of neutrons.

$II$. Only one isotope of an element can be stable and non-radioactive.

$III$. All elements have isotopes.

$IV$. All isotopes of carbon can form chemical compounds with oxygen-$16$.

Choose the correct option regarding an isotope.

The transition from the state $n = 4$ to $n = 3$ in a hydrogen-like atom results in ultraviolet radiation. Infrared radiation will be obtained in the transition

What does it mean if the $\alpha -$ particle passes through the foil of gold ?