Quantum Mechanics - Laser

The approximate number of photons in a femtosecond (10⁻¹⁵ s) pulse of 600 nanometers wavelength light from a 10-kilowatt peak-power dye laser is

A. 10³
B. 10⁷
C. 10¹¹
D. 10¹⁵
E. 10¹⁸

(GR9677 #59)

Solution:

Number of photon, n = E_total / E_single

Energy of a single photon,  E_single = hc/λ 

h = 6.63 × 10⁻³⁴ Js
c = 3 × 10⁸ m/s
λ  =  600 nanometers = 600 × 10⁻⁹ m

→ E_single = 3 × 10⁻¹⁹  J

From Power, P = W/t = E_total/t

→ Total energy, E_total =  Pt

P = 10 kW = 10⁴ W
t = 10⁻¹⁵ s

→ E_total = 10⁻¹¹ J

n = E_total / E_single = 10⁻¹¹  / (3 × 10⁻¹⁹)  = 0.3 × 10⁸ = 3 × 10⁷  J

Answer: B

Nuclear & Particle Physics - Spin

The ground state of the helium atom is a spin

A. singlet
B. doublet
C. triplet
D. quartet
E. quintuplet

(GR9277 #59)

Solution:

Spectroscopic notation: N^2s+1 L_j

2s + 1 = multiplicity

Singlet: 2s + 1 = 1, s = 0
Doublet: 2s + 1 = 2, s = 1/2
Triplet: 2s + 1 = 3, s = 1

Electron configuration of Helium: 1s²

Pauli Exclusion Principle: no two electrons can have exactly the same quantum number.

m_s1 =  ½  and m_s2 =  −½
Total spin quantum number, s = ½ + (−½) = 0
Multiplicity, 2 · 0 + 1 = 1 → Singlet

Answer: A 

Electromagnetism - LC circuit

For an inductor and capacitor connected in series, the equation describing the motion of charge is

where L is the inductance, C is capacitance, and Q is the charge. An analogous equation can be written for a simple harmonic oscillator with position x, mass m, and spring constant k. Which of the following correctly lists the mechanical analogs of L, C, and Q? 

	L	C	Q
A	m	k	x
B.	m	1/k	x
C.	k	x	m
D.	1/k	1/m	x
E.	x	1/k	1/m

(GR0177 #59)

Solution:

The form of SHO:

LC circuit equation: 

L = m
C = 1/k
Q = x

Answer: B