In an nmr experiment, the rf source oscillates at 38 mhz and the magnetic resonance of the hydrogen atoms in the sample being investigated occurs when the external field has magnitude 0.75 t. assume that the internal and external magnetic fields are both along a z axis, with the external field in the positive direction, and take the proton magnetic moment component μz to be 2.30 × 10-26 j/t. what is the z component of the internal magnetic field?

Bint = 0.204T

Explanation:

From the question, given that;

the RF source oscillates at 38MHz.

The external field has a magnitude of 0.75T.

From the relationship between external and internal magnetic field,

the external magnetic field is along the positive z-axis, while the internal field is along the positive z-axis.

From the expression;

Bnet = Bext - Bint (1)

Proton magnetic moment along z - direction gives

U2 = 2.3×10^-26 J/T

U2 = rhi = r(h/2π)I(2)

Energy change when an external magnetic field is applied becomes

∆E = h∆r =

∆E = rh/2π Bnet

where Bnet = Bext - Bint = h∆r/2u

Bint = Bext - Bnet

Bint = Bext - h∆r/2u =

= 0.75 - ((6.61×10^-34)×(38×10^6))/(2×(2.3×10^-26))

Bint = 0.204T

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.