Answer:
A mass spectrometer uses a magnetic field to separate ions based on their mass-to-charge ratio. The mass of an ion can be calculated from its charge, velocity, and the radius of curvature of its path in the magnetic field, using the formula m = (qBv)/(2πr), where m is the mass, q is the charge, B is the magnetic field, v is the velocity, and r is the radius of curvature.
In this case, the magnetic field is 5.00 mT, the charge of the unknown particle is 2e, and its velocity is 100 m/s. The radius of curvature of the ion's path is measured to be 1.67 mm. Plugging these values into the formula above, we get:
m = (2e * 5.00 mT * 100 m/s) / (2π * 1.67 mm) = 0.24 g/mol
Therefore, the mass of the unknown particle is 0.24 g/mol.
To determine which element the particle is, we can use the periodic table to find an element with a mass-to-charge ratio of 0.24 g/mol. The element with the closest match is magnesium (Mg), which has a mass-to-charge ratio of 24.31 g/mol. Therefore, the unknown particle is likely to be a magnesium ion (Mg²⁺).