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Fundamental Physics Quick Reference
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1
Question
What is the elementary charge of an electron in coulombs?
Page 1
Answer
-1.602 × 10⁻¹⁹ C
2
Question
What is the electron's mass relative to a proton?
Page 1
Answer
1/1840 of proton mass
3
Question
What is the specific charge (charge-to-mass ratio) order of magnitude given for an electron?
Page 1
Answer
~1.75 × 10⁸ C/kg
4
Question
What constant equals the charge of one mole of electrons?
Page 1
Answer
Faraday ≈ 96,500 C (per mole of electrons)
5
Question
What length does 1 fermi correspond to in meters?
Page 1
Answer
1 fermi = 10⁻¹⁵ m
6
Question
Write the relativistic expression for mass as a function of velocity.
Page 1
Answer
m = m' / √(1 - (v/c)²)
7
Question
What empirical formula gives the nuclear radius as a function of mass number A?
Page 1
Answer
R = R₀ A^{1/3}, with R₀ ≈ 1.4 fermi
8
Question
Express photon energy in terms of wavelength and Planck's constant.
Page 1
Answer
E = hc/λ (also E = hf)
9
Question
What is Planck's constant value as given here (in SI units)?
Page 1
Answer
h = 6.64 × 10⁻³⁴ J·s
10
Question
Write the Einstein photoelectric energy balance equation shown.
Page 1
Answer
hν = hν₀ + ½ mv² (E = E₀ + K.E.)
11
Question
Provide the expression for kinetic energy in terms of momentum used here.
Page 1
Answer
K.E. = p² / (2m)
12
Question
What is the Bohr model expression for the electron orbital radius?
Page 1
Answer
r = 0.529 Å × n² / Z
13
Question
What is the Bohr orbital speed formula shown (numerical factor times Z/n)?
Page 1
Answer
v = 2.18 × 10⁶ × (Z/n) m/s
14
Question
What is the Bohr energy level formula for hydrogen-like atoms in eV?
Page 1
Answer
E = -13.6 × (Z² / n²) eV
15
Question
State de Broglie's relation connecting wavelength and momentum.
Page 1
Answer
λ = h / (m c) (relativistic form here) or generally λ = h / p
16
Question
Which standing-wave condition relates orbit circumference to wavelength in Bohr's quantization?
Page 1
Answer
2πr = nλ
17
Question
Give Heisenberg's uncertainty relation as presented.
Page 1
Answer
Δx Δv ≥ h / (4π) (with Δv representing momentum uncertainty here)
18
Question
Relate energy expressions linking mass–energy and photon energy as listed.
Page 1
Answer
E = mc², E = hf, so hf = mc² and h c / λ = mc²
19
Question
How is energy in electronvolts related to wavelength in angstroms per the note?
Page 1
Answer
E (eV) = 12400 / λ (Å)
20
Question
What ratio of potential, kinetic, and total energy is given for bound systems?
Page 1
Answer
K.E. : P.E. : Total = -1 : 2 : 1 (convention indicating signs)
21
Question
According to the notes, on what variable does photocurrent depend?
Page 2
Answer
Photocurrent depends on light intensity (I)
22
Question
According to the photoelectric effect notes, which variable determines the kinetic energy of emitted electrons?
Page 2
Answer
Kinetic energy depends on frequency of incident light
23
Question
Write the formula provided for the number of spectral lines between two principal levels n1 and n2.
Page 2
Answer
Number of lines = (Δn (Δn + 1)) / 2, where Δn = n₂ - n₁
24
Question
Express the angular momentum magnitude for an electron in an orbital of quantum number l.
Page 1
Answer
L = (h / 2π) √[l(l+1)]
25
Question
Express the spin angular momentum magnitude for a particle with spin quantum number s.
Page 1
Answer
S = (h / 2π) √[s(s+1)]
26
Question
What is the relation between principal quantum number n and number of angular nodes and radial nodes as noted?
Page 1
Answer
Angular nodes = l; radial nodes = n - l - 1
27
Question
Convert the provided length scales: 10⁻¹² m, 10⁻¹⁵ m, 10⁻¹⁰ m, and 10⁻⁹ m to their named units.
Page 1
Answer
10⁻¹² m = picometer; 10⁻¹⁵ m = fermi (fm); 10⁻¹⁰ m = angstrom (Å); 10⁻⁹ m = nanometer (nm)
28
Question
What numerical value of Planck's constant in J·s appears repeatedly in the notes (rounded)?
Page 1
Answer
h ≈ 6.64 × 10⁻³⁴ J·s
29
Question
Using the Bohr energy formula, how does the energy change when n increases by a factor of 2 for hydrogen (Z=1)?
Page 1
Answer
Energy magnitude decreases by factor of 4 (E ∝ 1/n²)
30
Question
From Bohr speed formula, how does electron speed scale with principal quantum number n for fixed Z?
Page 1
Answer
v ∝ 1/n (inverse proportionality)