Rutherford scattering and Bohr model of the atom - One Line Questions
1.
What is the ground state energy of a hydrogen atom according to Bohr's model? —
-13.6 eV
2.
The energy of the electron in the second excited state (n=3) of hydrogen atom is: —
-1.51 eV
3.
For a hydrogen atom, the radius of the first Bohr orbit (n=1) is approximately 0.53 Å. What is the radius of the third Bohr orbit (n=3)? —
4.77 Å
4.
The Bohr radius (a₀) is defined as the radius of the ground state orbit of hydrogen. Its value is approximately: —
0.53 Å
5.
In Rutherford scattering, the number of particles scattered through an angle θ is proportional to: —
1/sin⁴(θ/2)
6.
The ionization energy of hydrogen is the energy required to excite the electron from the ground state (n=1) to the state where it is free from the nucleus (n=∞). Its value is: —
13.6 eV
7.
The transition from n=∞ to n=1 in a hydrogen atom corresponds to the emission of a photon of energy: —
13.6 eV
8.
The energy levels of a hydrogen atom are given by E_n = -13.6/n² eV. What is the energy required to excite an electron from the n=2 state to the n=4 state? —
2.55 eV
9.
If an electron in a hydrogen atom is in the n=4 state, how many different wavelengths of photons can be emitted as it transitions to lower energy states? —
6
10.
The total number of spectral lines observed when electrons transition from n=5 to the ground state (n=1) in a sample of hydrogen atoms is: —
10
11.
When an electron jumps from a higher energy orbit to a lower energy orbit, the atom: —
Emits energy in the form of a photon
12.
According to Bohr's model, electrons revolve around the nucleus in: —
Specific, stable, non-radiating orbits called stationary states
13.
Bohr's model is based on the postulates derived from: —
A combination of classical physics and quantum postulates
14.
For a large impact parameter in Rutherford scattering, the deflection angle is: —
Close to 0 degrees
15.
For a hydrogen-like atom with atomic number Z, the energy of the nth orbit is given by: —
E_n = -13.6 Z²/n² eV
16.
In Rutherford scattering, if the energy of the incident alpha particle is E, the cross-section for scattering at angle θ is proportional to: —
1 / (E² sin⁴(θ/2))
17.
Bohr's model introduced the concept of quantization of: —
Angular momentum only
18.
The angular momentum of an electron in the first Bohr orbit (n=1) of hydrogen is: —
h/2π
19.
Bohr's model is not applicable to: —
Atoms with more than one electron
20.
If the kinetic energy of the alpha particle is doubled, the distance of closest approach in Rutherford scattering will: —
Decrease by a factor of 2
21.
In Rutherford's scattering experiment, alpha particles are bombarded on a thin gold foil. What is the primary reason for the deflection of alpha particles? —
Interaction with the nucleus of the gold atoms
22.
Bohr's model could not explain the relative intensities of spectral lines because: —
It did not provide a mechanism for radiative transitions.
23.
What did Rutherford's experiment conclude about the positive charge in an atom? —
It is concentrated in a very small region at the center.
24.
Bohr's model is a semi-classical model because: —
It uses classical concepts of force and motion throughout.
25.
If the kinetic energy of an alpha particle is K, and it is directed towards a nucleus of charge Ze, the maximum kinetic energy it can lose at the point of closest approach (head-on collision) is: —
K
26.
Bohr's quantization condition states that the angular momentum (L) of an electron in a stationary orbit is quantized. It is given by: —
L = mvr = n(h/2π)
27.
Which of the following quantities is conserved in Rutherford scattering? —
All of the above
28.
Which spectral series of hydrogen lies in the infrared region? —
Paschen series
29.
The most significant observation in Rutherford's alpha particle scattering experiment was: —
All of the above.
30.
In Bohr's model, the energy of an electron in the nth orbit of a hydrogen atom is proportional to: —
1/n^2
31.
The radius of the nth orbit in Bohr's model for a hydrogen atom is proportional to: —
n^2
32.
The de Broglie wavelength associated with an electron in the nth Bohr orbit of hydrogen is proportional to: —
n
33.
The Balmer series of spectral lines for hydrogen corresponds to transitions from higher energy levels to which principal quantum number level? —
n=2
34.
The Pfund series of spectral lines for hydrogen corresponds to transitions from higher energy levels to which principal quantum number level? —
n=5
35.
Which of the following transitions in a hydrogen atom will emit a photon in the ultraviolet region of the electromagnetic spectrum? —
n=2 to n=1
36.
The ratio of the radius of the nth orbit to the radius of the mth orbit in a hydrogen atom is: —
n²/m²
37.
In Bohr's model, the frequency of revolution of an electron in the nth orbit is proportional to: —
Z²/n³
38.
Rutherford's model is also known as the: —
Planetary model
39.
In the Bohr model, for a hydrogen-like atom (atomic number Z), the radius of the nth orbit is given by: —
r_n = a₀ (n²/Z)
40.
If the radius of the first Bohr orbit is R₀, then the radius of the second Bohr orbit of hydrogen is: —
4R₀
41.
In Rutherford scattering, the number of scattered alpha particles detected at an angle θ is proportional to: —
1/sin⁴(θ/2)
42.
According to Rutherford's atomic model, the atom is mostly: —
Empty space with a small, dense nucleus
43.
What is the impact parameter (b) in Rutherford scattering? —
The perpendicular distance between the initial velocity vector of the alpha particle and the center of the nucleus.
44.
Rutherford's model of the atom failed to explain: —
The stability of the atom
45.
Bohr's model successfully explained: —
The discrete line spectrum of hydrogen
46.
The distance of closest approach in Rutherford scattering is the minimum distance between the alpha particle and the target nucleus when the alpha particle is directed head-on towards the nucleus. This distance is proportional to: —
The inverse of the kinetic energy of the alpha particle
47.
According to Bohr's postulate, an electron does not radiate energy while revolving in a stationary orbit because: —
The orbit is a stable, non-radiating state.
48.
What is the velocity of an electron in the nth Bohr orbit of hydrogen? —
v_n ∝ Z/n
49.
The energy difference between two adjacent Bohr orbits is related to the frequency (ν) of the emitted or absorbed photon by: —
ΔE = hν
50.
What is the angular frequency of revolution of an electron in the nth Bohr orbit of hydrogen? —
ω ∝ Z² / n³