Final answer:
In a TOF mass spectrometer, the distance traveled by a 25Mg+ ion can be calculated by finding its velocity using the formula for kinetic energy and then using the formula for distance traveled. The distance traveled by the ion is approximately 41.9 meters.
Step-by-step explanation:
In a TOF (Time of Flight) mass spectrometer, ions are accelerated to the same kinetic energy (KE). The formula for kinetic energy is KE = 1/2mv² where m is the mass of the ion and v is its velocity.
Given that each 25Mg+ ion is accelerated to a kinetic energy of 4.52 x 10⁻¹⁶ J, we can use the formula to find the velocity of the ion. Rearranging the formula, we have v = √(2KE/m).
Using the given values, the velocity of the ion is v = √(2 x 4.52 x 10⁻¹⁶ J / 25 x 1.67 x 10⁻²⁷ kg). Calculating this, we find that the velocity of the ion is approximately 2.91 x 10⁶ m/s.
The distance (d) traveled by the ion in the TOF drift region can be calculated using the formula v = d/t, where v is the velocity and t is the time of flight. Rearranging the formula, we have d = v x t.
Plugging in the values, the distance traveled by the ion is d = (2.91 x 10⁶ m/s) x (1.44 x 10⁻⁵ s) ≈ 41.9 meters.