Calculation of Difference in Energies of Protons Oriented with and Against Magnetic Field Strength of 1.50 T:

The energy difference between protons oriented with and against magnetic field strength can be calculated using the following formula:

ΔE = γBh

Where ΔE is the energy difference, γ is the gyromagnetic ratio of the proton, B is the magnetic field strength, and h is the Planck's constant.

Calculation:

Given, magnetic field strength (B) = 1.50 T

Gyromagnetic ratio of the proton (γ) = 2.68 x 10^8 rad T^-1 s^-1

Planck's constant (h) = 6.626 x 10^-34 J s

Substituting the values in the formula, we get:

ΔE = (2.68 x 10^8 rad T^-1 s^-1) x (1.50 T) x (6.626 x 10^-34 J s)

ΔE = 6.34 x 10^-26 J

Therefore, the difference in energies of protons oriented with and against magnetic field strength of 1.50 T is 6.34 x 10^-26 J.

Explanation:

When a proton is placed in a magnetic field, it experiences a torque and precesses around the magnetic field lines. The energy of the proton is dependent on its orientation with respect to the magnetic field.

When the proton is oriented with the magnetic field, it has lower energy than when it is oriented against the magnetic field. The energy difference between the two orientations can be calculated using the gyromagnetic ratio of the proton, magnetic field strength, and Planck's constant.

This energy difference is important in various applications such as magnetic resonance imaging (MRI) where protons in the body are aligned with an external magnetic field and then subjected to a radio frequency pulse to induce a change in their energy levels. The energy released during relaxation of the protons is detected by the MRI scanner to produce an image.