Q: A heat lamp produces 32.8 W of power at a wavelength of 6.5 $\mu$m. How many photons are emitted per second? ($h = 6.626 \times 10^{-34}$ J·s, $c = 3.00 \times 10^8$ m/s)

$1.07 \times 10^{20}$ photons/s

Question 1

Which of the following statements best describes the relationship between wavelength ($\lambda$) and frequency ($
u$) of electromagnetic radiation?

Accepted Answer

Wavelength and frequency are inversely proportional, as given by $
u = \dfrac{c}{\lambda}$.

Question 2

A laser emits green light with a wavelength of 515 nm. What is the frequency of this light? ($c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$5.83 	imes 10^{14}$ Hz

Question 3

Which experiment provided evidence for the particle nature of light?

Accepted Answer

The photoelectric effect

Question 4

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

Accepted Answer

$E = h
u$

Question 5

A heat lamp produces 32.8 W of power at a wavelength of 6.5 $\mu$m. How many photons are emitted per second? ($h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

$1.07 	imes 10^{20}$ photons/s

Question 6

Why do elements emit discrete wavelengths of light rather than a continuous spectrum?

Accepted Answer

Because electrons occupy quantized energy levels and transitions between these levels produce photons of specific energies.

Question 7

According to the Bohr model, what happens when an electron moves from a higher to a lower energy orbit?

Accepted Answer

Light is emitted with energy equal to the difference between the two orbits.

Question 8

Calculate the wavelength of light absorbed when an electron in a hydrogen atom transitions from $n=2$ to $n=7$. ($E = -2.18 	imes 10^{-18} \dfrac{1}{n^2}$ J, $h = 6.626 	imes 10^{-34}$ J·s, $c = 3.00 	imes 10^8$ m/s)

Accepted Answer

397 nm

Question 9

Which limitation of the Bohr model led to the development of quantum mechanics?

Accepted Answer

It could not explain the emission spectra of multi-electron atoms.

Question 10

The de Broglie wavelength of an object is given by:

Accepted Answer

$\lambda = \dfrac{h}{mv}$

Question 11

Which statement best describes the Heisenberg Uncertainty Principle?

Accepted Answer

The more precisely the position of a particle is known, the less precisely its momentum can be known.

Question 12

How many orbitals are present in the $n=3$ shell?

Accepted Answer

9

Question 13

Which quantum number determines the shape of an atomic orbital?

Accepted Answer

Angular momentum quantum number ($l$)

Question 14

What is the maximum number of orbitals in a $d$ subshell?

Accepted Answer

5

Question 15

Which of the following is true about the Pauli Exclusion Principle?

Accepted Answer

No two electrons in an atom can have the same four quantum numbers.

Question 16

What is the number of radial nodes in a 3s orbital?

Accepted Answer

2

Question 17

Which quantum number is associated with the orientation of an orbital in space?

Accepted Answer

Magnetic quantum number ($m_l$)

Question 18

What is the significance of the phase of atomic orbitals in chemical bonding?

Accepted Answer

It determines whether electrons interact constructively or destructively.

Question 19

Which of the following best describes the difference between paramagnetic and diamagnetic substances?

Accepted Answer

Paramagnetic substances have unpaired electrons and are attracted to magnetic fields; diamagnetic substances have all electrons paired and are not attracted.

Question 20

Which principle states that electrons fill orbitals from lowest to highest energy?

Accepted Answer

Aufbau principle

Quantum-Mechanical Model of the Atom: Study Notes

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