Atoms — Class 12 Physics PYQs

Atomic spectral emission lines of hydrogen atom are incident on a zinc surface. The lines which can emit photoelectrons from the surface are members of
(A) Balmer series
(B) Paschen series
(C) Lyman series
(D) Neither Balmer, nor Paschen nor Lyman series

The energy of an electron in a hydrogen atom in ground state is -13.6 eV. Its energy in an orbit corresponding to quantum number n is -0.544 eV. The value of n is
(A) 2
(B) 3
(C) 4
(D) 5

Assertion (A) : In Bohr model of hydrogen atom, the angular momentum of an electron in $n^{th}$ orbit is proportional to the square root of its orbit radius $r_n$.
Reason (R) : According to Bohr model, electron can jump to its nearest orbits only.

Assertion (A) : The potential energy of an electron revolving in any stationary orbit in a hydrogen atom is positive.
Reason (R) : The total energy of a charged particle is always positive.

Prove that, in Bohr model of hydrogen atom, the time period of revolution of an electron in $n^{th}$ orbit is proportional to $n^3$.

The energy of an electron in an orbit of Bohr hydrogen atom is -3.4 eV. Find its angular momentum.

The transition of electron that gives rise to the formation of the second spectral line of the Balmer series in the spectrum of hydrogen atom corresponds to :
(A) n${}_f$ = 2 and n${}_i$ = 3
(B) n${}_f$ = 3 and n${}_i$ = 4
(C) n${}_f$ = 2 and n${}_i$ = 4
(D) n${}_f$ = 2 and n${}_i$ = $\infty$

Energy levels A, B and C of an atom correspond to increasing values of energy i.e. E${}_A$ < E${}_B$ < E${}_C$. Let ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ be the wavelengths of radiation corresponding to the transitions C to B, B to A and C to A, respectively. The correct relation between ${\lambda }_1$, ${\lambda }_2$ and ${\lambda }_3$ is :
(A) ${\lambda }_1^2+{\lambda }_2^2={\lambda }_3^2$
(B) $\frac{1}{{\lambda }_1}+\frac{1}{{\lambda }_2}=\frac{1}{{\lambda }_3}$
(C) ${\lambda }_1+{\lambda }_2+{\lambda }_3=0$
(D) ${\lambda }_1+{\lambda }_2={\lambda }_3$

An alpha particle approaches a gold nucleus in Geiger-Marsden experiment with kinetic energy K. It momentarily stops at a distance d from the nucleus and reverses its direction. Then d is proportional to :
(A) $\frac{1}{\sqrt{K}}$
(B) $\sqrt{K}$
(C) $\frac{1}{K}$
(D) K

In Bohr model of hydrogen atom, find the ratio of period of revolution of the electron in the orbit n = 2 to that in the orbit n = 1.