Purpose: Self-check before the unit test. Constants: \(c=3.00\times10^8\,\text{m/s}\), \(h=6.63\times10^{-34}\,\text{Jยทs}\), \(m_e=9.11\times10^{-31}\,\text{kg}\), \(1\,\text{eV}=1.60\times10^{-19}\,\text{J}\).
๐ Formulae \(\gamma = 1/\sqrt{1-v^2/c^2}\) | \(\Delta t=\gamma\Delta t_0\) | \(L=L_0/\gamma\) | \(E_0=mc^2\) | \(E_k = hf - W\) | \(\lambda=h/p\) | \(E_n=-13.6/n^2\,\text{eV}\) | \(N=N_0(1/2)^{t/T_{1/2}}\)
Q1 โ Lorentz factor
Calculate \(\gamma\) for \(v=0.60c\). (2 decimals)
Answer:
Check
Solution
Solution:
\(\gamma=1/\sqrt{1-0.36}=1/\sqrt{0.64}=1.25\).
Q2 โ Time dilation
A muon at \(v=0.99c\) has rest half-life \(1.56\,\mu\text{s}\). What is its dilated half-life as measured in the lab? (ฮผs)
Answer:
ฮผs
Check
Solution
Solution:
\(\gamma = 1/\sqrt{1-0.9801}=7.09\). \(\Delta t = 7.09\cdot 1.56=11.06\,\mu\text{s}\).
Q3 โ Length contraction
A spaceship has rest length \(120\,\text{m}\). It moves at \(0.80c\) relative to a station. What length does the station observer measure? (m)
Answer:
m
Check
Solution
Solution:
\(\gamma = 1/0.6 = 1.667\). \(L = 120/1.667 = 72\,\text{m}\).
Q4 โ Mass-energy equivalence
How much energy (in J) is released by converting \(1.0\,\text{g}\) of mass entirely to energy?
Answer:
J
Check
Solution
Solution:
\(E = mc^2 = (10^{-3})(3\times10^8)^2 = 9\times10^{13}\,\text{J}\).
Q5 โ Photon energy
Compute the energy (eV) of a UV photon with frequency \(1.5\times10^{15}\,\text{Hz}\).
Answer:
eV
Check
Solution
Solution:
\(E = hf = (6.63\times10^{-34})(1.5\times10^{15}) = 9.945\times10^{-19}\,\text{J} = 6.21\,\text{eV}\).
Q6 โ Photoelectric KE
Light of frequency \(1.0\times10^{15}\,\text{Hz}\) hits a metal with work function \(W = 2.5\,\text{eV}\). Find the maximum KE of ejected electrons in eV.
Answer:
eV
Check
Solution
Solution:
\(hf = (6.63e{-}34)(10^{15})/1.6e{-}19 = 4.14\,\text{eV}\). \(KE = 4.14-2.5 = 1.64\,\text{eV}\).
Q7 โ de Broglie wavelength
An electron has speed \(2.0\times10^6\,\text{m/s}\). Find its de Broglie wavelength (ร10โปยนโฐ m).
Answer:
ร10โปยนโฐ m
Check
Solution
Solution:
\(\lambda = h/(mv) = 6.63e{-}34/(9.11e{-}31\cdot2\times10^6) = 3.64\times10^{-10}\,\text{m}\).
Q8 โ Bohr atom transition
An electron in hydrogen falls from \(n=3\) to \(n=2\). Calculate the photon energy emitted in eV.
Answer:
eV
Check
Solution
Solution:
\(\Delta E = -13.6(1/9 - 1/4)= -13.6(-5/36) = 1.89\,\text{eV}\) (H-ฮฑ, red).
Q9 โ Half-life
A radioactive isotope has \(T_{1/2}=12\,\text{years}\). Starting with \(800\,\text{g}\), how much remains after \(48\,\text{years}\)? (g)
Answer:
g
Check
Solution
Solution:
\(48/12 = 4\) half-lives. \(800 \times (1/2)^4 = 800/16 = 50\,\text{g}\).
๐ Self-Reflection
Rate your confidence (1 = need help, 4 = mastered):
1 2 3 4 5.1 Special relativity (time, length, mass-energy)
1 2 3 4 5.2 Photoelectric effect & photons
1 2 3 4 5.3 de Broglie & wave-particle duality
1 2 3 4 5.4 Bohr atom & spectra
1 2 3 4 5.5 Nuclear decay & half-life
SPH4U โ Physics, Grade 12 | Unit 5: Modern Physics โ AS Learning | Ontario Curriculum 2008