Classical Mechanics - Linear Momentum

A helium atom, mass 4u travels with non relativistic speed v normal to the surface of a certain material, makes an elastic collision with an (essentially free) surface atom, and leaves in the opposite direction with speed 0.6v. The atom on the surface must be an atom of

A. Hydrogen, mass 1u
B. Helium, mass 4u
C. Carbon, mass 12u
D. Oxygen, mass 16u
E. Silicon, mass 28u

(GR9677 #20)

Solution:

m_a = 4u
v_a  = v
v_b  = 0
v_a' = − 0.6v

Conservation of momentum of the system:

m_av_a + m_bv_b = m_av_a' + m_bv_b' 
4uv = 4u(− 0.6v) + m_bv_b' 
4uv = − 2.4uv  + m_bv_b' 
m_bv_b' = 6.4uv (Eq.1)

Conservation of kinetic energy of the system:

½ m_av_a² + ½ m_bv_b² = ½ m_av_a'² + ½ m_bv_b'²
4uv² = 4u(− 0.6v)² + m_bv_b'²
4uv² = 4u(0.36v²) + m_bv_b'²
m_bv_b'² =  4uv²  − 1.44uv²
m_bv_b'² =  2.56uv² (Eq.2)

(Eq.1) → (Eq.2)
6.4 (v_b') = 2.56v
v_b' =  (2.56/6.4)v = 0.4v  (Eq.3)

(Eq.3) → (Eq.1)
m_b = 6.4uv / 0.4v = 16u

Answer: D

Optics - Interference

In a double-slit interference experiment, d is the distance between the centers of the slits and w is the width of each slit, as shown in the figure above. For incident plane waves, an interference maximum on a distant screen will be “missing” when

A. d = √2 w
B. d = √3 w
C. 2d = w
D. 2d = 3w
E. 3d = 2w

(GR9277 #20)

Solution:

For double-slit interference, d is always bigger than w
→ (C) and (E) are FALSE

Constructive or destructive patterns of interference (single or double slits) only deals with integer and half integer factors.
→ (A) and (B) are FALSE

Answer: D


Calculation:

“missing” = destructive pattern (minimum intensity).
For double slit: d sin θ = (m + ¹/₂) λ; m = 0, 1, 2, 3, ...
For single slit: w sin θ = mλ; m = 1, 2, 3, ...

^d/_w =  (m + ¹/₂)/m
Take m = 1,
^d/_w = ³/₂
2d = 3w

Special Relativity - Speed of Kaon

A positive kaon (K⁺) has a rest mass of 494 MeV/c² , whereas a proton has a rest mass of 938 MeV/c². If a kaon has a total energy that is equal to the proton rest energy, the speed of the kaon is most nearly

A. 0.25c
B. 0.40c
C. 0.55c
D. 0.70c
E. 0.85c

(GR8677 #20)

Solution:





Answer: E

Nuclear & Particle Physics - X-rays

In the production of X-rays, the term “bremsstrahlung” refers to which of the following?

1. The cut-off wavelength, λ_min, of the X-ray tube
2. The discrete X-ray lines emitted when an electron in an outer orbit fills a vacancy in an inner orbit of the atoms in the target metal of the X-ray tube
3. The discrete X-ray lines absorbed when an electron in an inner the X-ray tube
4. The smooth, continuous X-ray spectra produced by high-energy blackbody radiation from the X-ray tube
5. The smooth, continuous X-ray spectra produced by rapidly decelerating electron in the target metal of the X-ray tube

(GR0177 #20)

Solution:

Bremsstrahlung is German for ‘braking radiation’.

This is the radiation that is released as the electron slows down or is “braked” and results in a continuous spectra.

Answer: E