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In hydrogen-like atoms, the ratio of difference of energies ${\mathrm{E}}_{4\mathrm{n}} - {\mathrm{E}}_{2\mathrm{n}} \mathrm{and} {\mathrm{E}}_{2\mathrm{n}} - {\mathrm{E}}_{\mathrm{n}}$ varies with atomic number z and principal quantum number n as
1. $\frac{{\mathrm{z}}^2}{{\mathrm{n}}^2}$
2. $\frac{{\mathrm{z}}^4}{{\mathrm{n}}^4}$
3. z/n
4. none of these

A hydrogen atom is in an excited state of principal quantum number n. It emits a photon of wavelength $\mathrm{\lambda }$ when returns to the ground state. The value of n is (R = Rydberg constant)
1. $\sqrt{\mathrm{\lambda R}\left(\mathrm{\lambda R} - 1\right)}$
2. $\sqrt{\frac{\left(\mathrm{\lambda R} - 1\right)}{\mathrm{\lambda R}}}$
3. $\sqrt{\frac{\mathrm{\lambda R}}{\left(\mathrm{\lambda R} - 1\right)}}$
4. $\sqrt{\left(\mathrm{\lambda R} - 1\right)}$

A sample contains 16 g of a radioactive material, the half-life of which is 2 days. After 32 days the amount of radioactive material left in the sample is
1. Less than 1 mg
2. (1/4) g
3. (1/2) g
4. 1 g

A freshly radioactive source half-life 2hr emits radiation of intensity which is 64 times the permissible safe level. The minimum time after which it would be possible to work safely with this source is
1. 6 hr
2. 12 hr
3. 2 hr
4. 128 hr 

IF photons of energy 12.75 eV are passing through hydrogen gas in ground state then no. of lines in emission spectrum will be 
1. 6
2. 4
3. 3
4. 2

The half-life of a radioactive element ${}_{222}\mathrm{R}_{\mathrm{u}}$ is 3.8 hrs. Mass of this element which has activity equal to ${10}^{16}$ Rutherford is
(1) 0.37 kg
(2) 0.37 g
(3) 0.073 g
(4) 0.07g

An electron collides with a fixed hydrogen atom in its ground state. hydrogen atom gets excited and the colliding electron loses all its kinetic energy. Consequently, the hydrogen atom may emit a photon corresponding to the largest wavelength of the Balmer series. The minimum kinetic energy of the colliding electron is
1.  10.2 eV
2.  1.9 eV
3.  12.09 eV
4.  13.6 eV

If doubly ionized lithium atom is hydrogen-like with atomic number 3, the wavelength of radiation required to excite the electron in ${\mathrm{Li}}^{++}$ from the first to the third Bohr and the number of different spectral lines observed in the emission spectrum of the above-excited system are
1. 296 A, 6
2. 114 A, 3
3. 1026 A, 6
4. 8208 A, 3

Uranium ores contain one radium-226 atom for every 2.8 x ${10}^5$ Uranium-238 atoms. Calculate the half-life of ${}_{92}\mathrm{U}_{238}$ given that the half-life of ${}_{88}\mathrm{R}_{226}$ is 1600 years and ${}_{88}\mathrm{R}_{226}$ is a decay product of ${}_{92}\mathrm{U}_{238}$.
(1) 1.75 x ${10}^3$ years
(2) 1600 x $\frac{238}{92}$ years
(3) 4.5 x ${10}^9$ years
(4) 1600 x $\frac{92}{238}$ years

As per the Bohr model, the minimum energy (in eV) required to remove an electron from the ground state of doubly ionized Li and (Z = 3) is
1.  1.51
2.  13.6
3.  40.8
4.  122.4 

In Bohr's model, the atomic radius of the first orbit is $r_0$, then the radius of hte third orbit is
1.  $\frac{r_0}{9}$
2.  $r_0$.  
3.  9$r_0$
4.  3$r_0$

A particle of mass 3m at rest decays into two particles of masses m and 2m having non-zero velocities. The ratio of the de-Broglie wavelengths of the particles $({\mathrm{\lambda }}_1/{\mathrm{\lambda }}_2)$ is
1. 1/2
2. 1/4
3. 2
4. None of these

As per Bohr model, the minimum energy (in eV) required to remove an electron from the ground state of doubly ionized Li and (Z = 3) is
1.  1.51
2.  13.6
3.  40.8
4.  122.4

In the hydrogen atom spectrum, ${\mathrm{\lambda }}_{3 - 1} \mathrm{and} {\mathrm{\lambda }}_{2 - 1}$ represent wavelengths emitted due to transition from second and first excited states to the ground state respectively. The value of $\frac{{\mathrm{\lambda }}_{3 - 1}}{{\mathrm{\lambda }}_{2 - 1}}$ is
1. 27/32
2. 32/27
3. 4/9
4. 9/4

Nuclei of a radioactive element A is being produced at a constant rate $\mathrm{\alpha }$. The element A has a decay constant $\mathrm{\lambda }$. At time t = 0, there are ${\mathrm{N}}_0$ nuclei of the element A. The number of nuclei of A at time t is
1. $\frac{1}{\mathrm{\lambda }}\left[\alpha - \left(\alpha - \lambda N_0\right)e^{-\lambda t}\right]$
2. $\frac{1}{\mathrm{\lambda }}\left[\left(\alpha - \lambda N_0\right)e^{-\lambda t}\right]$
3. $\lambda \left[\alpha - \left(\alpha - \lambda N_0\right)e^{\lambda t}\right]$
4. $\lambda N_0{e}^{\mathit{-}\lambda t}$

There are two radioactive nuclei A and B. A is an alpha emitter and B is a beta emitter. If their disintegration constants are in the ratio 1 : 2, then the rato of atoms of A and B at any time t so that probabilities of getting alpha and beta particles are same at that instant 
1.  2 : 1
2.  1 : 2
3.  e
4.  $e^{-1}$

The radius of the hydrogen atom in its ground state is $5.3\times {10}^{-11}$m. After a collision with an electron, it is found to have a radius of $21.2\times {10}^{-11}$m. What is the principal quantum number of the final state of the atom?
1.  n = 4
2.  n = 2
3.  n = 16
4.  n = 3 

Electrons in hydrogen atom revolve in radius 0.53 A (in ground state). Due to collision, electron starts revolving in radius of 4.77 A. Change in angular momentum of the electron will be equal to
 
(1) $$2.11×10${}^{-36}$kg $m^2$/sec
(2) $$4.22×10${}^{-30}$g $m^2$/sec
(3) $$2.11×10${}^{-27}$g c$m^2$/sec
(4) $$4.22×10${}^{-36}$kg $m^2$/sec

Radioactive material has life's for $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ emission equal to 20 and 100 yrs respectively. $\frac{1}{8}$th fraction of the radioactive material will be remain there after
1.  360 yrs
2.  50 yrs
3.  120 yrs
4.  180 yrs 

An electron in H-atom jumps from the second excited state to the first excited state and then from first excited to ground state. Let the ratio of wavelength, momentum and energy of photons emitted in these two cases be a, b and c respectively. Then, choose the incorrect answer:
1.$\mathrm{c}=\frac{1}{\mathrm{a}}$
2. $\mathrm{a}=\frac{9}{4}$
3. $\mathrm{b}=\frac{5}{27}$
4. $\mathrm{c}=\frac{5}{27}$