Final answer:
To find the magnetic field in the mass spectrometer for an ionized molecule of isoflurane, we use the Lorentz force related to the centripetal force required to keep the molecule in a circular path. By equating the force formulas, we calculate the magnetic field using the mass, charge, velocity, and radius of the isoflurane molecule's path.
Step-by-step explanation:
The question is asking us to calculate the magnitude of the magnetic field (B) in a mass spectrometer that anesthesiologists use to monitor respiratory gases during surgery. Specifically, it asks for the magnetic field required to keep an ionized molecule of isoflurane on a circular path. To solve this, we can use the formula for the Lorentz force, which in the case of a charged particle moving in a magnetic field, is given by F = qvB, where q is the charge, v is the velocity, and B is the magnetic field. The centripetal force needed to keep the particle on a circular path is given by F = (mv^2)/r, where m is the mass of the particle, v is the velocity, and r is the radius of the path.
Equate both expressions for force to solve for B,
B = (mv)/(qr)
where:
- m = 3.06×10⁻²⁵ kg (mass of isoflurane molecule)
- q = +e = 1.60×10⁻ C (charge of a proton)
- v = 7.30×10³ m/s (speed of the ionized molecule)
- r = 0.124 m (radius of the circular path)
Plugging the values in,
B = (3.06×10⁻²⁵ kg × 7.30×10³ m/s) / (1.60×10⁻ C × 0.124 m)
The answer gives us the magnitude of the magnetic field needed to maintain the circular path of ionized isoflurane in the mass spectrometer.