Q 31 :

The radius of $2^{\text{nd}}$ orbit of ${\mathrm{He}}^{+}$ of Bohr's model is $r_1$ and that of fourth orbit of ${\mathrm{Be}}^{3+}$ is represented as $r_2$. Now the ratio $\frac{r_2}{r_1}$ is $x:1$. The value of $x$ is _________    [2023]

Q 32 :

In hydrogen atom spectrum, $(R\to \text{Rydberg's constant})$

A.   the maximum wavelength of the radiation of Lyman series is $\frac{4}{3R}$
B.   the Balmer series lies in the visible region of the spectrum
C.   the minimum wavelength of the radiation of Paschen series is $\frac{9}{R}$
D.   the minimum wavelength of Lyman series is $\frac{5}{4R}$

Choose the correct answer from the options given below:                             [2026]

• A, B Only

   

• A, B and C Only

   

• A, B and D Only

   

• B, D Only

   

Q 33 :

Two electrons are moving in orbits of two hydrogen-like atoms with speeds $3\times {10}^5\text{\hspace{0.05em}m/s}$ and $2.5\times {10}^5\text{\hspace{0.05em}m/s}$ respectively. If the radii of these orbits are nearly same, then the possible order of energy states are _______ respectively.             [2026]

• 8 and 10

   

• 6 and 5

   

• 10 and 12

   

• 9 and 8

   

Q 34 :

The energy of an electron in an orbit of the Bohr’s atom is $-0.04E_{0}eV$ where $E_0$ is the ground state energy. If L is the angular momentum of the electron in this orbit and h is the Planck’s constant, then $\frac{2\pi L}{h}=$_____.   [2026]

• 5

   

• 2

   

• 6

   

• 4

   

Q 35 :

An atom ${}_3{}^{8}X$ is bombarded by shower of fundamental particles and in 10 s this atom absorbed 10 electrons, 10 protons and 9 neutrons. The percentage growth in the surface area of the nucleons is recorded by:  [2026]

• 900%

   

• 250%

   

• 150%

   

• 225%