Atoms

A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the nth orbit and the particle's speed v in the orbit depend on n as

1. r n2/3; v n1/3
2. r n4/3; v n-1/3
3. r n1/3; v n1/3
4. r n1/3; v n2/3

De-Broglie wavelength of an electron orbiting in the n = 2 state of hydrogen atom is close to (Given Bohr radius = 0.052 nm)

1. 1.67 nm
2. 2.67 nm
3. 0.067 nm
4. 0.67 nm

Given below are two statements: In the light of the above statements, choose the most appropriate answer from the options given below.

1. Both Statement I and Statement II are correct
2. Both Statement I and Statement II are incorrect
3. Statement I is correct but Statement II is incorrect
4. Statement I is incorrect but Statement II is correct

Match List I with List II: Choose the correct answer from the options given below:

1. A-II, B-I, C-IV, D-III
2. A-III, B-IV, C-II, D-I
3. A-IV, B-III, C-I, D-II
4. A-I, B-II, C-III, D-IV

The spectral series which corresponds to the electronic transition from the levels n2 = 5, 6, to the level n1 = 4 is

1. Pfund series
2. Brackett series
3. Lyman series
4. Balmer series

Some energy levels of a molecule are shown in the figure with their wavelengths of transitions. Then : [figure]

1. 3 > 2, 1 = 2 2
2. 3 > 2, 1 = 4 2
3. 1 > 2, 2 = 2 3
4. 2 > 1, 2 = 2 3

In hydrogen spectrum, the shortest wavelength in the Balmer series is . The shortest wavelength in the Brackett series is :

1. 4
2. 9
3. 16
4. 2

The radius of inner most orbit of hydrogen atom is 5.3 10-11 m. What is the radius of third allowed orbit of hydrogen atom?

1. 1.06 Å
2. 1.59 Å
3. 4.77 Å
4. 0.53 Å

Let T1 and T2 be the energy of an electron in the first and second excited states of hydrogen atoms, respectively. According to the Bohr's model of an atom, the ratio T1 : T2 is

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

Let R1 be the radius of the second stationary orbit and R2 be the radius of the fourth stationary orbit of an electron in Bohr's model. The ratio R1R2 is :

1. 4
2. 0.25
3. 0.5
4. 2