Q: Which equation can be used to calculate the wavelength of a spectral line in the Balmer series of hydrogen?

$\nu = 3.2881 \times 10^{15} \text{ s}^{-1} \left( \dfrac{1}{2^2} - \dfrac{1}{n^2} \right)$, where $n > 2$

Question 1

Which experiment led to the discovery of the atomic nucleus, and what was the key observation that supported this discovery?

Accepted Answer

The Gold Foil Experiment, where most alpha particles passed through the foil but some were deflected at large angles.

Question 2

Which of the following statements best describes the difference between the Thomson and Rutherford models of the atom?

Accepted Answer

The Thomson model described the atom as a uniform sphere of positive charge with embedded electrons, while the Rutherford model proposed a dense nucleus surrounded by electrons.

Question 3

Electromagnetic radiation can be described by its wavelength ($\lambda$), frequency ($
u$), and speed ($c$). Which equation correctly relates these quantities?

Accepted Answer

$c = \lambda 
u$

Question 4

A sodium vapor lamp emits light with a wavelength of 589 nm. What is the frequency of this radiation? (Speed of light $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$
u = 5.09 	imes 10^{14}$ Hz

Question 5

Which phenomenon provides evidence for the wave nature of light?

Accepted Answer

Diffraction and interference patterns observed in Young's double slit experiment.

Question 6

According to Planck's quantum theory, what is the energy of a photon with frequency $
u$?

Accepted Answer

$E = h 
u$

Question 7

The photoelectric effect demonstrates that electromagnetic radiation has which property?

Accepted Answer

Particle-like properties, as photons can eject electrons from a metal surface.

Question 8

Which statement about atomic emission spectra is correct?

Accepted Answer

Each element produces a unique set of discrete spectral lines, acting as an atomic fingerprint.

Question 9

The Bohr model of the hydrogen atom postulates that the energy of the electron in the $n$th orbit is given by $E_n = -\dfrac{R_H}{n^2}$. What does the negative sign indicate?

Accepted Answer

The electron is bound to the nucleus and its energy is lower than that of a free electron.

Question 10

Which transition in the hydrogen atom would emit a photon with the highest energy?

Accepted Answer

From $n=2$ to $n=1$

Question 11

Which equation can be used to calculate the wavelength of a spectral line in the Balmer series of hydrogen?

Accepted Answer

$
u = 3.2881 	imes 10^{15} 	ext{ s}^{-1} \left( \dfrac{1}{2^2} - \dfrac{1}{n^2} ight)$, where $n > 2$

Question 12

Which quantum number primarily determines the size and energy of an atomic orbital?

Accepted Answer

Principal quantum number ($n$)

Question 13

In multi-electron atoms, why do $s$ orbitals have lower energy than $p$, $d$, and $f$ orbitals within the same principal shell?

Accepted Answer

Because $s$ orbitals penetrate closer to the nucleus and experience less shielding.

Question 14

Which quantum number describes the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number ($m_\ell$)

Question 15

What is the maximum number of electrons that can occupy a single orbital?

Accepted Answer

2

Question 16

Which effect explains why electrons in outer shells experience a reduced attraction to the nucleus in multi-electron atoms?

Accepted Answer

Shielding effect

Question 17

Which statement about the energy levels in the hydrogen atom is correct?

Accepted Answer

Energy levels are quantized and only certain values are allowed.

Question 18

Which quantum number is associated with the shape of atomic orbitals?

Accepted Answer

Angular momentum quantum number ($\ell$)

Question 19

Which of the following best describes the difference between atomic emission spectra and continuous spectra?

Accepted Answer

Atomic emission spectra consist of discrete lines unique to each element, while continuous spectra contain all wavelengths.

Question 20

Which real-world application relies on the unique atomic emission spectra of elements?

Accepted Answer

Identifying elements in distant stars using astronomical spectroscopy.

Atoms: The Quantum World – Electronic Structure and Quantum Theory

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