Characteristics of Bohr's Atomic Model

Q.

The average kinetic energy of translation of a molecule of an ideal gas at temperature T is:

1. (1/2) kT

2. (7/2) kT

3. (3/2) kT

4. (5/7) kT

Q. Bohr's model is applicable only to one electron atoms like helium He⁺ and lithium Li⁺⁺ apart from hydrogen atom.

1. True
2. False

Q. The energy of the ground electronic state of hydrogen atom is -13.6 eV. The energy of the first excited stae will be :

1. – 52.4 eV
2. – 27.2 eV
3. – 68 eV
4. – 3.4 eV

Q. If the energy absorbed by each X2 molecule of a gas is 3.5% 10-19 J and the bond energy of X2 is 180.6 kJ mol-1 then the kinetic energy per atom will be (1) 2.5 x 10-19 J (3) 2.5 x 10-20 J (2) 5.0 x 10-20 J (4) 1.5x10-19 J

Q.

The expected energy of the electrons at absolute zero is called?

Q. What is the energy of state in a triply ionised berrylium $\left(B{e}^{+++}\right)$ whose radius is equal to that of ground state of hydrogen?

1. 27.2 eV
2. 54.4 eV
3. 13.6 eV
4. 40.8 eV

Q. The frequency of the first line in Lyman series in the hydrogen spectrum is $v$. What is the frequency of the corresponding line in the spectrum of doubly ionized Lithium?

1. $v$
2. $3v$
3. $9v$
4. $27v$

Q. Okay I will give you another easy one. Just one last.
Find the angular momentum of the electron in $2^{nd}$ orbit of $H{e}^{+}$ ion.

1. $\frac{h}{2\pi }$
2. $\frac{h}{\pi }$
3. $\frac{2h}{\pi }$
4. $\frac{4h}{\pi }$

Q. In the Bohr's hydrogen atom model, the radius of the stationary orbit is directly proportional to (n = principle quantum number)

1. $n$
2. $n^{-1}$
3. $n^2$
4. $n^{-2}$

Q. According to Bohr's theory, the radius of the $n^{th}$ orbit of an atom of atomic number Z is proportional to

1. $\frac{n^2}{Z^2}$
2. $\frac{n^2}{Z}$
3. $\frac{n}{Z}$
4. $n^2{Z}^2$

Q. An electron in a hydrogen atom makes a transition $n_1\to n_2$ where $n_1$ and $n_2$ are principal quantum numbers of the states. Assume the Bhor's model to be valid. The time period of the electron in the initial states is eight times to that of final state. What is ratio of $\frac{n_1}{n_2}$

1. 8 : 1
2. 4 : 1
3. 2 : 1
4. 1 : 2

Q. An electron jumps from the $4^{th}$ orbit to the $2^{nd}$ orbit of hydrogen atom. Given the Rydberg's constant $R={10}^{5}c{m}^{-1}$. The frequency in Hz of the emitted radiation will be

1. $\frac{3}{16}\times {10}^5$
2. $\frac{3}{16}\times {10}^{15}$
3. $\frac{9}{16}\times {10}^{15}$
4. $\frac{3}{4}\times {10}^{15}$

Q. The energy required to knock out the electron in the third orbit of a hydrogen atom is equal to

1. $13.6eV$
2. $+\frac{13.6}{9}eV$
3. $-\frac{13.6}{3}eV$
4. $-\frac{3}{13.6}eV$

Q. what is the average kinetic energy of a diatomic gas molecule at 25 degree Celsius given k- 1.38 x 10 raised to -23

Q. Calculate the kinetic energy per molecule of a gas at 127C.Given the boltzman constant K=12038*10*-23 mass of each molecule of a gas is 6.4*10*-27?

Q. 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

1. one
2. two
3. three
4. four

Q. If 13.6 ev energy is required to ionise the hydrogen atom, then the energy required to remove an electron from first exited state (n = 2) is

1. 10.2 eV
2. 0 eV
3. 3.4 eV
4. 6.8 eV

Q. According to Bohr's theory, the radius of the $n^{th}$ orbit of an atom of atomic number Z is proportional to

1. $\frac{n^2}{Z^2}$
2. $\frac{n^2}{Z}$
3. $\frac{n}{Z}$
4. $n^2{Z}^2$

Q. The ratio of kinetic energy to the total energy of an electron in a Bohr's orbit of the hydrogen atom is

1. 1 : 1
2. 1 : -1
3. 2 : -1
4. 1 : -2

Q. The kinetic energy of the electron in an orbit of radius r in hydrogen atom is (e = electronic charge)

1. $\frac{e^2}{r^2}$
2. $\frac{e^2}{2r}$
3. $\frac{e^2}{r}$
4. $\frac{e^2}{2r^2}$

Q. When an electron in hydrogen atom is excited, from its $4^{th}$ to $5^{th}$ stationary orbit, the change in angular momentum of electron is (Planck’s constant:$h=6.6\times {10}^{-34}J-s$)

1. $4.16\times {10}^{-34}J-s$
2. $3.32\times {10}^{-34}J-s$
3. $1.05\times {10}^{-34}J-s$
4. $2.08\times {10}^{-34}J-s$

Q. The ionisation energy of 10 times ionised sodium atom (given the ionisation energy of H atom is 13.6eV) is

1. $13.6eV$
2. $13.6\times 11eV$
3. $\frac{13.6}{11}eV$
4. $13.6\times (11{)}^{2}eV$

Q. The wavelength of radiation emitted is ${\lambda }_0$ when an electron jumps from the third to the second orbit of hydrogen atom. For the electron jump from the fourth to the second orbit of the hydrogen atom, the wavelength of radiation emitted will be

1. $$\frac{16}{25}{\lambda }_0$$
2. $$\frac{20}{27}{\lambda }_0$$
3. $$\frac{27}{20}{\lambda }_0$$
4. $$\frac{25}{16}{\lambda }_0$$

Q. The ratio of the energies of the hydrogen atom in its first to second excited state is

1. $\frac{1}{4}$
2. $\frac{4}{9}$
3. $\frac{9}{4}$
4. $4$

Q. Ratio of minimum of Lyman & Balmer wavelengths series for hydrogen atom is

1. 1 : 4
2. 2 : 9
3. 4 : 3
4. 7 : 9

Q. In a Bohr atom the electron is replaced by a particle of mass 150 times the mass of the electron and the same charge. If $a_0$ is the radius of the Bohr orbit, then that of the new atom will be

1. $150a_0$
2. $\sqrt{150}{a}_0$
3. $\frac{a_0}{\sqrt{150}}$
4. $\frac{a_0}{150}$

Q. Calculate the KEper molecule and also r.m.s velocity of a gas at 127 ^oC.Given k_b =1.38 x 10 ^-23 J/molecule K& mass per molecule of the gas= 6.4x 10 ^-27kg

Q. An electron jumps from the $4^{th}$ orbit to the $2^{nd}$ orbit of hydrogen atom. Given the Rydberg's constant $R={10}^{5}c{m}^{-1}$. The frequency in Hz of the emitted radiation will be

1. $\frac{3}{16}\times {10}^5$
2. $\frac{3}{16}\times {10}^{15}$
3. $\frac{9}{16}\times {10}^{15}$
4. $\frac{3}{4}\times {10}^{15}$

Q. The wavelength of the second line in Balmer series of the hydrogen spectrum is 486.4 nm. What is the wavelength of the first line of the Lyman series?

1. 121.6 nm
2. 364.8 nm
3. 729.6 cm
4. None of these

Q. The radius of electron's second stationary orbit in Bohr's atom is R. The radius of the third orbit will be

1. $3R$
2. $2.25R$
3. $9R$
4. $\frac{R}{3}$