boltz - E 1 . The population difference divided by the sum...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
Physics 225/315 Feb. 15, 2008 State Populations in Magnetic Field The energy difference between the two energy levels of a magnetic moment of a spin 1/2 particle in a magnetic field B 0 is Δ E = ¯ 0 ω 0 = - γB 0 Assume B 0 = 1 Tesla Δ E = ¯ hc c ω 0 2 π ω 0 42 MHz Δ E 200 eV - nm 3 10 8 10 9 2 π 42 10 6 Hz 1 . 8 10 - 7 eV At room temperature kT 1 / 40 eV Δ E kT 40 × 1 . 8 10 - 7 7 10 - 6 The probability of a two state system being in a state with energy E 0 is 1 Z e - E 0 /kT where Z = e - E 0 /kT + e - E 1 /kT see Moore, Volume T, Example T6.2 The lower energy state (with the larger population) has energy E 0 and the higher,
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: E 1 . The population difference divided by the sum of the populations is P-P 1 P + P 1 = e-E /kT-e-E 1 /kT e-E /kT + e-E 1 /kT = 1-e-( E 1-E ) /kT 1 + e-( E 1-E ) /kT ≈ 1-e Δ E/kT 2 ≈ Δ E 2 kT ≈ 3 . 5 10-6 Thus only about one in a million molecules contribute to the next magnetization of the sample. However there are of order 10 23 molecules present so the signal is due to about 10 17 magnetic moments....
View Full Document

This note was uploaded on 03/01/2010 for the course PHYSICS 225 taught by Professor Rothberg during the Spring '10 term at University of Washington.

Ask a homework question - tutors are online