Question

The frequency of the applied RF signal used to excite spins is directly proportional to the magnitude of the static magnetic field used to align the spins, with proportionality constant 5 hz/T. If the strength of the applied field is known to be 20 T plus or minus 3 T, which of the following correctly describes the uncertainty in the INVERSE frequency (1/frequency)?
A. 3/2000s
B. 3/5s
C. 1/15s
D. 1/4

Answer 1

Complete Question

The complete question is shown on the first uploaded image  

Answer:

The uncertainty in inverse frequency is  $\Delta [\frac{1}{w} ]= \frac{3}{2000} \ s$

Explanation:

From the question we are told that

   The value of the proportionality constant is  $k = 5 \frac{Hz }{T}$

   The strength of the magnetic field is  $B = 20 \ T$

   The change in this strength of magnetic field is  $\Delta B = 3 \ T$

The magnetic field is given as

           $B = \frac{k}{\frac{1}{w} }$

Where $w$ is frequency

The uncertainty or error of the field is given as

         $\Delta B = \frac{k }{[\frac{1}{w}^]^2 } \Delta [\frac{1}{w} ]$

The uncertainty in inverse frequency is given  as

           $\Delta [\frac{1}{w} ] = \frac{\Delta B}{k [\frac{1}{w^2} ]}$

                    $\Delta [\frac{1}{w} ]= \frac{\Delta B}{k (B)^2 }$

substituting values

                  $\Delta [\frac{1}{w} ]= \frac{3}{5 (20)^2 }$

               $\Delta [\frac{1}{w} ]= \frac{3}{2000} \ s$